applications of trigonometry case study questions term 2

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Class 10 Maths: Case Study Questions of Chapter 9 Some Applications of Trigonometry PDF

Case study Questions on the Class 10 Mathematics Chapter 9  are very important to solve for your exam. Class 10 Maths Chapter 9 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Some Applications of Trigonometry Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 9 Some Applications of Trigonometry

Case Study/Passage Based Questions

There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing on the top of a 50 m high temple, observed from the top that the angle of depression of the top and foot of other temples are 30° and 60° respectively.

The measure of ∠ADF is equal to (a) 45° (b) 60° (c) 30° (d) 90°

Answer: (c) 30°

A measure of ∠ACB is equal to (a) 45° (b) 60° (c) 30° (d) 90°

Answer: (b) 60°

Width of the river is (a) 28.90 m (b) 26.75 m (c) 25 m (d) 27 m

Answer: (a) 28.90 m

The height of the other temple is (a) 32.5 m (b) 35 m (c) 33.33 m (d) 40 m

Answer: (c) 33.33 m

The angle of depression is always (a) reflex angle (b) straight (c) an obtuse angle (d) an acute angle

Answer: (d) an acute angle

Rohit is standing at the top of the building observes a car at an angle of 30°, which is approaching the foot of the building at a uniform speed. 6 seconds later, the angle of depression of the car formed to be 60°, whose distance at that instant from the building is 25 m.

The height of the building is (a) 25√2 m (b) 50 m (c) 25√3 m (d) 25 m

Answer: (c) 25√3 m

Distance between two positions of the car is (a) 40 m (b) 50 m (c) 60 m (d) 75 m

Answer: (b) 50 m

Total time is taken by the car to reach the foot of the building from the starting point is (a) 4 secs (b) 3 secs (c) 6 secs (d) 9 secs

Answer: (d) 9 secs

The distance of the observer from the car when it makes an angle of 60° is (a) 25 m (b) 45 m (c) 50 m (d) 75 m

Answer: (c) 50 m

The angle of elevation increases (a) when point of observation moves towards the object (b) when point of observation moves away from the object (c) when object moves away from the observer (d) None of these

Answer: (a) when point of observation moves towards the object

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Maths Some Applications of Trigonometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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CBSE Class 10 Maths Case Study Questions for Chapter 9 - Some Applications of Trigonometry (Published By CBSE)

Check case study questions for cbse class 10 maths chapter 9 - some applications of trigonometry. these questions are published by the cbse itself for class 10 students..

Case study based questions are new for class 10 students. Therefore, it is quite essential that students practice with more of such questions so that they do not have problem in solving them in their Maths board exam. We have provided here the case study questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry. All these questions have been published by the Central Board of Secondary Education (CBSE) for the class 10 students. Therefore, students must solve all the questions seriously so that they may score the desired marks in their Maths exam.

Check Case Study Questions for Class 10 Maths Chapter 9:

CASE STUDY 1:

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

1. What is the angle of elevation if they are standing at a distance of 42m away from the monument?

Answer: b) 45 o

2. They want to see the tower at an angle of 60 o . So, they want to know the distance where they should stand and hence find the distance.

Answer: a) 25.24 m

3. If the altitude of the Sun is at 60 o , then the height of the vertical tower that will cast a shadow of length 20 m is

a) 20√3 m

b) 20/ √3 m

c) 15/ √3 m

d) 15√3 m

Answer: a) 20√3 m

4. The ratio of the length of a rod and its shadow is 1:1. The angle of elevation of the Sun is

5. The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is

a) corresponding angle

b) angle of elevation

c) angle of depression

d) complete angle

Answer: a) corresponding angle

CASE STUDY 2:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi(height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of the two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains.

1. The distance of the satellite from the top of Nanda Devi is

a) 1139.4 km

b) 577.52 km

d) 1025.36 km

Answer: a) 1139.4 km

2. The distance of the satellite from the top of Mullayanagiri is

Answer: c) 1937 km

3. The distance of the satellite from the ground is

Answer: b) 577.52 km

4. What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

5.If a mile stone very far away from, makes 45 o to the top of Mullanyangiri mountain. So, find the distance of this mile stone from the mountain.

a) 1118.327 km

b) 566.976 km

Also Check:

Case Study Questions for All Chapters of CBSE Class 10 Maths

Tips to Solve Case Study Based Questions Accurately

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Case Study on Some Applications of Trigonometry Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Some Applications of Trigonometry Class 10 Maths can use this page to download the PDF file. 

The case study questions on Some Applications of Trigonometry are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Some Applications of Trigonometry case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Some Applications of Trigonometry Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Some Applications of Trigonometry, therefore, they prepared a set of solutions along with the case study questions on Some Applications of Trigonometry.

The case study on Some Applications of Trigonometry Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Some Applications of Trigonometry case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Some Applications of Trigonometry Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Some Applications of Trigonometry case study questions on Class 10 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Some Applications of Trigonometry Case study questions as it will help better prepare for the Class 10 board exam preparation.
• Develop Problem-Solving Skills: Class 10 Maths Some Applications of Trigonometry case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
• Understand Real-Life Applications: Several Some Applications of Trigonometry Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Some Applications of Trigonometry as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Some Applications of Trigonometry?

Students can choose their own way to answer Case Study on Some Applications of Trigonometry Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Some Applications of Trigonometry Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Some Applications of Trigonometry questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Some Applications of Trigonometry Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Some Applications of Trigonometry?

 A few essential things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry are -

• Basic Formulas of Some Applications of Trigonometry: One of the most important things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry is to learn about the basic formulas or revise them before solving the case-based questions on Some Applications of Trigonometry.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Some Applications of Trigonometry case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Some Applications of Trigonometry Class 10 Maths?

Use Selfstudys.com to find Case Study on Some Applications of Trigonometry Class 10 Maths. For ease, here is a step-wise procedure to download the Some Applications of Trigonometry Case Study for Class 10 Maths in PDF for free of cost.

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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [Term 2]

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Question 13 - Case Study - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [Term 2] - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. A guard, stationed at the top of a 240m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer is an instrument used fo measuring angles or slopes(tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be 30°.(Lighthouse of Mumbai Harbour. Picture credits - Times of India Travel) i) Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.

Ii) after 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(√3 - 1) m. he immediately raised the alarm. what was the new angle of depression of the boat from the top of the observation tower.

This question is similar to Ex 9.1, 13 Chapter 9 Class 10 - Some Applications of Trigonometry

Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. A guard, stationed at the top of a 240m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer is an instrument used fo measuring angles or slopes(tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be 30°. (Lighthouse of Mumbai Harbour. Picture credits - Times of India Travel) i) Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower. ii) After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(√3 - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower? Making a labelled figure Given that height of the lighthouse is 240 m Hence, AC = 240 m And angle of depression of boat is 30° So, ∠ PAB = 30 ° Since Angle of depression = Angle of elevation ∴ ∠ ABC = 30° Question 13 (i) Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower. We need to find distance between boat and tower, i.e. BC In right angled triangle ΔABC, tan B = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵) tan 30° = 𝐴𝐶/𝐵𝐶 (" " 1)/√3 = (" " 240)/𝐵𝐶 BC = 240√𝟑 m Question 13 (ii) After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(√3−1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower? Let Boat be now at point D Since Distance of tower is reduced by 240(√3−1) m Hence, BD = 𝟐𝟒𝟎(√𝟑−𝟏) m Let angle of depression of boat now be θ So, ∠ PAD = θ ° Since Angle of depression = Angle of elevation ∴ ∠ ADC = θ Also, CD = BC − BD = 240√3 −240(√3−1) = 240√3 −240√3+240 = 𝟐𝟒𝟎 m Now, In right angled triangle ΔABC, tan D = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵) tan θ = 𝐴𝐶/𝐶𝐷 tan θ = 𝟐𝟒𝟎/𝟐𝟒𝟎 tan θ = 1 ∴ θ = 45° Thus, required angle of depression is 45°

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• Class 10 Maths

Important Questions Class 10 Maths Chapter 9 Applications of Trigonometry

Important questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry are provided here for the board exams preparation. The questions are based on the new pattern of CBSE and are as per the revised syllabus. Students who are preparing CBSE 2022-2023 Maths exam are advised to practice these important questions of Some Applications of Trigonometry For Class 10 . Solving these questions will help students to score high marks in the questions asked from this chapter.

Trigonometry has more applications in our daily existence, and hence, the chapter is crucial for the board exam and valuable in many other fields. Most of the questions from this chapter are also asked in the competitive exams such as JEE etc.

• Applications of Trigonometry
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Below, we have provided the questions of Chapter 9 Applications of Trigonometry with the solutions. Students can als o find additional qu estions without solutions for their practice.

Important Questions & Answers For Class 10 Maths Chapter 9 – Some Applications of Trigonometry

Q.1: The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

Let AB be the tower and BC be the length of its shadow when the sun’s altitude (angle of elevation from the top of the tower to the tip of the shadow) is 60° and DB be the length of the shadow when the angle of elevation is 30°.

Let us assume, AB = h m, BC = x m

DB = (40 +x) m

In the right triangle ABC,

tan 60° = AB/BC

h = √3 x……….(i)

In the right triangle ABD,

tan 30° = AB/BD

1/√3 =h/(x + 40) ……..(ii)

From (i) and (ii),

x(√3 )(√3 ) = x + 40

3x = x + 40

Substituting x = 20 in (i),

Hence, the height of the tower is 20√3 m.

Q. 2: A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Using given instructions, draw a figure. Let AC be the broken part of the tree. Angel C = 30 degrees.

To Find: Height of the tree, which is AB

From figure: Total height of the tree is the sum of AB and AC i.e. AB+AC

In right ΔABC,

Using Cosine and tangent angles,

cos 30° = BC/AC

We know that, cos 30° = √3/2

√3/2 = 8/AC

AC = 16/√3 …(1)

tan 30° = AB/BC

1/√3 = AB/8

AB = 8/√3 ….(2)

From (1) and (2),

Total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.

Q. 3: Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Let AB and CD be the poles of equal height.

O is the point between them from where the height of elevation is taken. BD is the distance between the poles.

As per the above figure, AB = CD,

OB + OD = 80 m

In right ΔCDO,

tan 30° = CD/OD

1/√3 = CD/OD

CD = OD/√3 … (1)

In right ΔABO,

tan 60° = AB/OB

√3 = AB/(80-OD)

AB = √3(80-OD)

AB = CD (Given)

√3(80-OD) = OD/√3 (Using equation (1))

3(80-OD) = OD

240 – 3 OD = OD

Substituting the value of OD in equation (1)

CD = 20√3 m

⇒ OB = (80-60) m = 20 m

Therefore, the height of the poles are 20√3 m and the distance from the point of elevation are 20 m and 60 m respectively.

Q. 4:  An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Let AB be the height of the observer and PR be the height of the tower.

Also, PB is the distance between the foot of the tower and the observer.

Consider θ as the angle of elevation of the top of the tower from the eye of the observer.

From the above figure,

AB = PQ = 1.5 m

PB = QA = 20 m

QR = PR – PQ = 22 – 1.5 = 20.5 m

In the right triangle AQR,

tan θ = QR/AQ

tan θ = 20.5/20.5 = 1

⇒ tan θ = tan 45°

Hence, the angle of elevation is 45°.

Q. 5: The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st.

Let BC = s; PC = t

Let the height of the tower be AB = h.

∠ABC = θ and ∠APC = 90° – θ

(∵ the angle of elevation of the top of the tower from two points P and B are complementary)

In triangle ABC,

tan θ = AC/BC = h/s ………..(i)

In triangle APC,

tan (90° – θ) = AC/PC = h/t

cot θ = h/t ………..(ii)

Multiplying (i) and (ii),

tan θ × cot θ = (h/s) × (h/t)

1 = h 2 /st

Hence, the height of the tower is √st.

Q.6: The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Let AB be the height of the tower.

The angle of elevation of the top of a tower from point P is 30°, i.e. ∠APB = 30°.

Given that, when the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°.

Thus, PQ = 20 m

Also, ∠AQB = 30° + 15° = 45°.

In right triangle ABQ,

tan 45° = AB/QB

h = x….(i)

In right triangle ABP,

tan 30° = AB/PB

1/√3 = h/(x + 20)

x + 20 = √3h  {from (i)}

h + 20 = √3h

√3h – h = 20

h = 20/(√3 – 1)

h = [20/(√3 – 1)] × [(√3 + 1)/(√3 + 1)]

= 20(√3 + 1)/(3 – 1)

= 20(√3 + 1)/2

= 10(√3 + 1)

Therefore, the height of the tower is 10(√3 + 1) m.

Q.7: A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

Let AB be the vertical pole and AC be the length of the rope.

Also, the angle of elevation = ∠ACB = 30°

In right triangle ABC,

sin 30 = AB/AC

1/2 = AB/20

AB = 20/2 = 10

Therefore, the height of the vertical pole is 10 m.

Q.8: From the top of a 7 m high building, the angle of elevation of the top of a cable tower is

60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Let AB be the height of the building and CE be the height of the tower.

Also, A be the point from where the elevation of the tower is 60° and the angle of depression of its foot is 45°.

EC = DE + CD

From the figure,

CD = AB = 7 m

tan 45° = AB/BC

BC = 7 {since BC = AD}

Thus, AD = 7 m

In right triangle ADE,

tan 60° = DE/AD

⇒ DE = 7√3 m

EC = DE + CD = (7√3 + 7) = 7(√3 + 1)

Therefore, the height of the tower is 7(√3 + 1) m.

Video Lesson on Applications of Trigonometry

Practice Questions For Class 10 Maths Chapter 9 Some Applications of Trigonometry

• The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill? [Answer: 150 m]
• A bridge across the river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river? [Answer: 75√2 m]
• There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are the points directly opposite to each other on the two banks, and in a line with the tree. If the angles of elevation of the top of the tree from P and Q are 30° and 45° respectively, find the height of the tree. [Answer: 36.6.m]
• From a point 20m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower. [Answer: 11.56 m]
• A flagstaff stands at the top of a 5m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flagstaff. [Answer: 3.65 m]
• A tower subtends an angle α at a point A in the place of its base and the angle of depression of the foot of the tower at a point b ft. just above A is β. Prove that the height of the tower is b tan α cot β.
• A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower. [Answer: 9.55m]
• The angle of elevation of a cloud from a point h metres above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ. Prove that the height of the cloud above the lake is h[(tan φ + tan θ)/ (tan φ – tan θ)].
• The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings. [Answer: 4(3 + √3) m]
• A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower at a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point. [Answer: 3 sec]

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Case Study Class 10 Maths Questions

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

I	NUMBER SYSTEMS	06
II	ALGEBRA	20
III	COORDINATE GEOMETRY	06
IV	GEOMETRY	15
V	TRIGONOMETRY	12
V	MENSURATION	10
VI	STATISTICS & PROBABILITY	11

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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Case Based Questions: Some Application of Trigonometry - Class 10 MCQ

15 questions mcq test - case based questions: some application of trigonometry.

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Read the following text and answer the following questions on the basis of the same. A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Q. Write the value of sec 30°.

Read the following text and answer the following questions on the basis of the same. A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Q. The line drawn from the eye of an observer to the point in the object viewed by the observer.

• A. horizontal line
• B. Vertical line
• C. Line of sight
• D. Parallel lines

Read the following text and answer the following questions on the basis of the same. A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Q. Find the time taken by the car to reach the foot of the tower from point D to B.

Let the speed of car be v m/s.

Let car takes t seconds to reach the point B from the point D

Distance travel by car in t sec = vt m.

In ΔABD, we have

h = √3 vt ...(i)

and in right D ABC, we have

Read the following text and answer the following questions on the basis of the same.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. Write the value of cosec 60°.

Q. If the two lines are parallel; then the alternate opposite angles are ..................... .

• A. different
• C. opposite
• D. None of these

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. What is the value of tan 45°?

AP = 10 √3 m

In right ΔPAD,

10 √3 = 10 + BD

BD = 10 √3 – 10

BD = 7.32 m.

• A. BP 2 = AB 2 + AP 2
• B. AB 2 = AP 2 + BP 2
• C. AP 2 = AB 2 + BP 2
• D. None of these.

Read the following text and answer the following questions on the basis of same.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

• A. Acute angled triangle
• B. Right angled triangle
• C. Obtuse angled triangle
• D. Equilateral triangle.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. The value of tan 45° is

The value of tan 45° is = 1

• A. 1(√3 + 1) m
• B. ( √3 +1) m
• C. ( √3 +2) m
• D. 3(√3 + 1) m

In ΔPDB, ∠B = 45°

tan 45° = PD/DB

width of the river = AB = AD + DB

= 3(√3 + 1)m.

• A. Perpendicular/Base
• B. Base/Perpendicular
• C. Hypotenuse/Base
• D. Perpendicular/Hypotenuse

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Class 10th Maths - Some Applications of Trigonometry Case Study Questions and Answers 2022 - 2023

By QB365 on 09 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 10th Maths Subject - Some Applications of Trigonometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Some applications of trigonometry case study questions with answer key.

10th Standard CBSE

Final Semester - June 2015

Case Study 

(ii) Measure of \(\angle\) ACB is equal to

(iii) Width of the river is 

(iv) Height of the other temple is

(v) Angle of depression is always

(ii) Value of DF is equal to

\((a) \frac{h}{\sqrt{3}} \mathrm{~m}\)

\((b) h \sqrt{3} \mathrm{~m}\)

\((c) \frac{h}{2} \mathrm{~m}\)

\((d) 2 h \mathrm{~m}\)

(iii) Value of h is

(iv) Height of the balloon from the ground is

(v) If the balloon is moving towards the building, then both angle of elevation will

\((a) 15 \mathrm{~m}\)	\((b) 15 \sqrt{2} \mathrm{~m}\)
\((c) \frac{15}{\sqrt{3}} \mathrm{~m}\)	\((d) \frac{15}{\sqrt{2}} \mathrm{~m}\)

(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

\((a) \frac{15}{\sqrt{2}} \mathrm{~m}\)

\((b) 15 \sqrt{2} \mathrm{~m}\)

\((c) 15 \mathrm{~m}\)

\((d) {15}{\sqrt{3}} \mathrm{~m}\)

(iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

(iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

(v) Which mathematical concept is used here?

(ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length of the ladder is

\((b) \frac{10}{\sqrt{3}} \mathrm{~m}\)

\((c) \frac{15}{\sqrt{2}} \mathrm{~m}\)

(iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find the height of the window. (Take \(\sqrt{3}\) = 1.73)

(iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is

(v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?

\(\sqrt{5}\)

(ii) What should be the length of ladder, so that it makes an angle of 60° with the ground?

\((a) 4\sqrt{3} {~m}\)

\((b) 2\sqrt{3} {~m}\)

\((c) 3\sqrt{3} {~m}\)

\((d) 5\sqrt{3} {~m}\)

(iii) The distance between the foot ofladder and pole is

\((a) 6\sqrt{3} {~m}\)

\((b) 4\sqrt{3} {~m}\)

\((c) 3\sqrt{3} {~m}\)

\((d) 2\sqrt{3} {~m}\)

(iv) What will be the measure of \(\angle\) BCD when BD and CD are equal?

(v) Find the measure of \(\angle\) DBC.

(ii) Distance between two positions of the car is

(iii) Total time taken by the car to reach the foot of the building from starting point is

(iv) The distance of the observer from the car when it makes an angle of 60° is

(v) The angle of elevation increases

(ii) If  \(\angle\) YAB = 30°, then \(\angle\) ABD is also 30°, Why?

(iii) Length of CD is equal to

(iv) Length of BD is equal to

m

m

(v) Length of AC is equal to

m

m

(ii) If the height of the pedestal is 20 m, then the height of the statue is

\((a) 20 \sqrt{3} \mathrm{~m}\)

\((b) 20(\sqrt{3}-1) \mathrm{m}\)

\((c) 20(\sqrt{3}+1) \mathrm{m}\)

\((d) 10(\sqrt{3}-1) \mathrm{m}\)

(iii) If the height of the statue is 1.6 m, then height of the pedestal is

\((a) 0.8(\sqrt{3}-1) \mathrm{m}\)

\((b) 1.6(\sqrt{3}+1) \mathrm{m}\)

\((c) 0.8(\sqrt{3}) \mathrm{m}\)

\((d) 0.8(\sqrt{3}+1) \mathrm{m}\)

(iv) If the total height of the statue and pedestal is 39 m, then find the length of AC.

(v) If the height of the pedestal is 35 m, then length of AD is

\((a) (\angle x, \angle y)\)

\((b) (\angle y, \angle z)\)

\((c) (\angle z, \angle t)\)

\((d) (\angle r, \angle q)\)

(ii) If the position of Pankaj is 25 m away from the base of pedestal and Zr = 30°, then find the height of pedestal.

(iii) If the height of pedestal is 30 m, \(\angle\) t = 45° and \(\angle\) z = 30°, then the horizontal distance between Arun and Pankaj is

(iv) If the vertical height of sky lantern from the top of pedestal is 12 m and \(\angle\) y = 30°, then distance between Teewan and sky lantern is

(v) If \(\angle\) q = 60° and position of Arun is 15 m away from the base of pedestal, then find the height of pedestal.

(ii) Find the length of RO.

(iii) The width of the road is

(iv) If the angle of elevation made by pole PQ is 45°, then the length of PO =

(v) Angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is known as

\((a) \sqrt{3} \mathrm{~m}\)

\((b) 30 \sqrt{3} \mathrm{~m}\)

\((c) \frac{30}{\sqrt{3}} \mathrm{~m}\)

(ii) If the top of broken part of a tree touches the ground at a point whose distance from foot of the tree is equal to height of remaining part, then its angle of inclination is

(iii) The angle of elevation are always

(v) If the height of a tree is 6 m, which is broken by wind in such a way that its top touches the ground and makes an angles 30° with the ground. At what height from the bottom of the tree is broken by the wind?

\((b) \frac{\sqrt{3}}{6} \mathrm{~m}\)

\((c) 6 \sqrt{3} \mathrm{~m}\)

\((d) \frac{6}{\sqrt{3}} \mathrm{~m}\)

(a) 6 m

\((b) 6 \sqrt{3} \mathrm{~m}\)

\((c) \sqrt{3} \mathrm{~m}\)

\((d) 10 \sqrt{3} \mathrm{~m}\)

(iii) Width of the river is

(iv) The angles of elevation and depression are always

(v) If BD = 21 m, then height of the bridge is

\((c) 7 \sqrt{3} \mathrm{~m}\)

\((d) \frac{7}{\sqrt{3}} \mathrm{~m}\)

(ii) The value of PD is

(v) If A and B are two objects and the eye of an observer is at point 0, then the line of sight will be

\((c) \frac{100}{\sqrt{3}} \mathrm{~m}\)

\((d) 100 \sqrt{3}\)

(ii) If the distance between the position of pigeon increases, then the angle of elevation

(iii) Find the distance between the boy and the pole.

\((b) \frac{50}{\sqrt{3}} \mathrm{~m}\)

\((c) 50 \sqrt{3} \mathrm{~m}\)

\((d) 60 \sqrt{3} \mathrm{~m}\)

(iv) How much distance the pigeon covers in 8 seconds?

(v) Find the speed of the pigeon

(ii) Find the length of GH.

(iii) The length of second step is 

(iv) The length of PQ =

(v) The length of first step is

*****************************************

Some applications of trigonometry case study questions with answer key answer keys.

(i) (b): The person who makes small angle of elevation is more closer to the balloon. \(\therefore\) Radlra is more closer to the balloon. (ii) (b):  \(\text { In } \Delta E F D, \tan 30^{\circ}=\frac{E D}{D F}\) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{h}{D F} \) \(\Rightarrow \quad D F=h \sqrt{3} \mathrm{~m}\) (iii) (a): In \(\Delta\) GCE, \(\begin{array}{l} \tan 60^{\circ}=\frac{E C}{G C}=\frac{h+4}{D F} \\ \Rightarrow \quad \sqrt{3}=\frac{h+4}{\sqrt{3} h} \Rightarrow 3 h=h+4 \Rightarrow h=2 \end{array}\) (iv) (c): Height of the balloon from the ground = BE = BC + CD + DE = 2 + 4 + 2 = 8 m (v) (b)

(i) (b): Total height of pole = 8 m \(\therefore\) BD = AD - AB = (8 - 2)m = 6 m (ii) (a):  \(\text { In } \Delta B D C, \frac{B D}{B C}=\sin 60^{\circ}\) \(\Rightarrow \quad \frac{6}{B C}=\frac{\sqrt{3}}{2} \) \(\Rightarrow \quad B C=\frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=4 \sqrt{3} \mathrm{~m}\) (iii) (d):  \(\text { In } \triangle B D C\) \(\frac{B D}{C D}=\tan 60^{\circ} \Rightarrow \frac{6}{C D}=\sqrt{3} \Rightarrow C D=\frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=2 \sqrt{3} \mathrm{~m}\) (iv) (b) :  \(\text { If } \Delta B C D\) \(\frac{B D}{C D}=\tan \theta \Rightarrow 1=\tan \theta \quad[\because B D=C D] \) \(\Rightarrow \quad \theta=45^{\circ}\) (v) (c) :   \(\operatorname{In} \Delta B D C, \angle B+\angle D+\angle C=180^{\circ}\) \(\therefore \quad \angle B=180^{\circ}-60^{\circ}-90^{\circ}=30^{\circ}\)

(i) (c):   \(\text { In } \Delta A B C, \frac{A B}{B C}=\tan 60^{\circ}\) \(\Rightarrow \quad A B=25 \times \sqrt{3}\) \(\therefore\) Height of building is 25 \(\sqrt{3}\) m . (ii) (b):   \(\text { In } \Delta A B D, \frac{A B}{B D}=\tan 30^{\circ}\) \(\Rightarrow \frac{25 \sqrt{3}}{B D}=\frac{1}{\sqrt{3}} \Rightarrow B D=75 \mathrm{~m}\) \(\therefore\)  Distance between two positions of car = (75 - 25) m = 50m. (iii) (d): Time taken to cover 50 m distance = 6 sec. \(\therefore\) Time taken to cover 25 m distance = 3 sec. \(\therefore\) Total time taken by car = 6 sec + 3 sec = 9 sec (iv) (c):  \(\text { In } \Delta A B C, \frac{B C}{A C}=\cos 60^{\circ}\) \(\Rightarrow \quad \frac{25}{A C}=\frac{1}{2} \) \(\Rightarrow A C=50 \mathrm{~m}\) (v) (a)

(i) (b):   \(\angle X A C=45^{\circ}\)   \(\therefore \quad \angle A C D=45^{\circ}\)   [Alternate interior angles] (ii) (b) (iii) (c) :  \(\text { In } \Delta A C D\) \(\frac{A D}{D C}=\tan 45^{\circ} \) \(\Rightarrow \frac{100}{D C}=1 \Rightarrow D C=100 \mathrm{~m}\) (iv) (d):   \(\text { In } \Delta A B D, \frac{A D}{B D}=\tan 30^{\circ}\) \(\Rightarrow \quad \frac{100}{B D}=\frac{1}{\sqrt{3}} \) \(\Rightarrow \quad B D=100 \sqrt{3} \mathrm{~m}\) (v) (a):  \(\text { In } \Delta A D C\) \(\frac{A D}{A C}=\sin 45^{\circ} \Rightarrow \frac{100}{A C}=\frac{1}{\sqrt{2}} \Rightarrow A C=100 \sqrt{2} \mathrm{~m}\)

(i) (c):   \(\text { In } \Delta O P Q\) ,  we have \(\tan 60^{\circ}=\frac{P Q}{P O} \) \(\Rightarrow \sqrt{3}=\frac{20}{P O} \) \(\Rightarrow P O=\frac{20}{\sqrt{3}} \mathrm{~m}\) (ii) (b): In \(\Delta\) ORS, we have \(\tan 30^{\circ}=\frac{R S}{O R} \Rightarrow \frac{1}{\sqrt{3}}=\frac{20}{O R} \Rightarrow O R=20 \sqrt{3} \mathrm{~m}\) (iii) (d): Clearly, width of the road = PR \(\begin{array}{l} =P O+O R=\left(\frac{20}{\sqrt{3}}+20 \sqrt{3}\right) \mathrm{m} \\ =20\left(\frac{4}{\sqrt{3}}\right) \mathrm{m}=\frac{80}{\sqrt{3}} \mathrm{~m}=46.24 \mathrm{~m} \end{array}\) (iv) (a):   \(\text { In } \Delta O P Q \text { , if } \angle P O Q=45^{\circ} \text { , then }\) \(\tan 45^{\circ}=\frac{P Q}{P O} \Rightarrow 1=\frac{20}{P O} \Rightarrow P O=20 \mathrm{~m}\) (v) (b)

(i) (d) : Clearly, \(\angle\) DAC = 60° So,in \(\Delta\) ADC, we have \(\tan 60^{\circ}=\frac{C D}{A D} \Rightarrow \sqrt{3}=\frac{6}{A D} \) \(\Rightarrow A D=\frac{6}{\sqrt{3}} \mathrm{~m}\) (ii) (b): Clearly, \(\angle\) DBC = 30° So, in  \(\Delta\) BDC,we have \(\tan 30^{\circ}=\frac{C D}{B D} \) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{6}{B D} \) \(\Rightarrow B D=6 \sqrt{3} \mathrm{~m}\) (iii) (b): Width of the river = AB = AD + BD \(\begin{array}{l} =\frac{6}{\sqrt{3}}+6 \sqrt{3} \\ =6\left(\frac{1}{\sqrt{3}}+\sqrt{3}\right)=6\left(\frac{4}{\sqrt{3}}\right)=\frac{24}{\sqrt{3}} \mathrm{~m}=13.87 \mathrm{~m} \end{array}\) (iv) (a): The angle of elevation and angle of depression are always acute angles. (v) (c): In \(\Delta\) BCD,if BD = 21m, then \( \tan 30^{\circ}=\frac{C D}{B D} \) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{C D}{21} \Rightarrow C D=\frac{21 \sqrt{3}}{3}=7 \sqrt{3} \mathrm{~m}\)

(i) (b): In the right   \(\Delta\) ADQ, we have \(\sin 30^{\circ}=\frac{D Q}{A D} \Rightarrow \frac{1}{2}=\frac{D Q}{24}\) \(\Rightarrow \quad D Q=12 \mathrm{~m}\) Thus, distance of paraglider from the ground is 12 m. (ii) (a): We have PQ = BC = 6 m Now, as DQ = 12 m \(\therefore\) DP = DQ - PQ = 12 - 6 = 6 m (iii) (c) : In right  \(\Delta\) BDP,we have \(\sin 45^{\circ}=\frac{D P}{B D} \Rightarrow \frac{1}{\sqrt{2}}=\frac{6}{B D}\) \(\Rightarrow \quad B D=6 \sqrt{2} \mathrm{~m}\) Thus, the distance of paraglider from the girl is 6 \(\sqrt{2}\)  m. (iv) (d): \(\angle\) AOP given in figure, is the angle of depression. (v) (c): If A and B are two objects and the eye of an observer is at point 0, then line of sight will be both OA and OB.

Given, side of square top = 2 m \(\therefore\) AB = HT = QR = CD = 2 m Also, A C and BD are perpendicular to the ground. So, AH = HQ = QC.  (By B.P.T. Theorem) (i) (b): \(\text { In } \triangle A E C\) \(\sin 60^{\circ}=\frac{A C}{A E} \Rightarrow \frac{\sqrt{3}}{2}=\frac{6}{A E} \Rightarrow A E=6.93 \mathrm{~m}\) \(\therefore\) Length of each leg i.e., AE = BF = 6.93 m. (ii) (c):   \(\text { In } \Delta A G H, \tan 60^{\circ}=\frac{A H}{G H} \Rightarrow \sqrt{3}=\frac{2}{G H}\) \(\Rightarrow G H=1.15 \mathrm{~m}\) (iii) (a) : Length of second step = GH + HT + TU = 1.15 + 2 + 1.15 = 4.3 m (iv) (b): \(\text { In } \Delta A P Q\) \(\tan 60^{\circ}=\frac{A Q}{P Q} \Rightarrow \sqrt{3}=\frac{4}{P Q} \Rightarrow P Q=\frac{4}{\sqrt{3}} \mathrm{~m}=2.31 \mathrm{~m}\) (v) (c) : Length of first step = PQ + QR + RS =2.31 + 2 + 2.31 = 6.62 m

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Case study class 10 Maths chapter 9?

Case study class 10 Maths chapter 9 Case study class 10 Maths chapter 9 Some Applications of Trigonometry Case study class 10 Maths Case study questions class 10 chapter 9 Maths for 2022-2023. Class 10 Maths Case study for second terminal exam 10th Maths solution 2022-2023 Case study class 10 chapter 9 Maths 2022-2023 class 10 chapter 9 study, class x Maths Case study class 10 chapter 9 Case study 2022-2023. Case study class 10 Maths chapter 9 Some Applications of Trigonometry

Case study Get Hindi Medium and English Medium for Class 10 Maths to download. Please follow the link to visit website for first and second term exams solutions. Class 10 Maths Solutions for second Term 2022-2023 https://www.tiwariacademy.com/ncert-solutions/class-10/maths/chapter-9/

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Class 10 Maths Case Study Questions Chapter 8 Introduction to Trigonometry

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• Post category: class 10th
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Case study Questions in the Class 10 Mathematics Chapter 8  are very important to solve for your exam. Class 10 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 8  Introduction to Trigonometry

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Introduction to Trigonometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 8 Introduction to Trigonometry

Case Study/Passage-Based Questions

Question 1:

(a) 2m

(b) 3m

(c) 4m

(d) 6m

Answer: (d) 6m

(ii) Measure of ∠A =

(a) 30°

(b) 60°

(c) 45°

(d) None of these

Answer: (c) 45°

(iii) Measure of ∠C =

(iv) Find the value of sinA + cosC.

(a) 0

(b) 1

(c) 1/2

(d) 2√2

Answer: (d) 2√2

(v) Find the value of tan 2 C + tan 2  A.

(a) 0

(b) 1

(c) 2

(d) 1/2

Answer: (c) 2

Question 2:

(a) 30°

(b) 45°

(c) 60°

(d) None of these

Answer: (a) 30°

(ii) The measure of  ∠C is

Answer: (c) 60°

(iii) The length of AC is 

(a)2√3 m

(b)√3m

(c)4√3m

(d)6√3m

Answer: (d)6√3m

(iv) cos2A =

(a) 0

(b)1/2

(c)1/√2

(d)√3/2

Answer: (b)1/2

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Introduction to Trigonometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case Study Questions for Class 10 Maths

• Last modified on: 1 year ago
• Reading Time: 13 Minutes

This article covers case study questions for Class 10 Maths. Students are suggested to go through all the questions to score better in the exams.

Why Students Fear Case Study Questions for Class 10 Maths?

Students may fear Case Study questions for Class 10 Maths for the following reasons:

• Application of Concepts: Case Study questions require the application of mathematical concepts to real-world situations. Students may find it difficult to apply the concepts they have learned to solve the given scenario.
• Limited Practice: Unlike other types of questions, students may have limited practice with Case Study questions. This lack of familiarity may cause anxiety and fear among students.
• Lengthy and Complex Scenarios: Case Study questions often present lengthy and complex scenarios, which can be overwhelming for students. They may struggle to identify the relevant information and apply the appropriate mathematical concepts.
• Time Pressure: Case Study questions may require more time to solve compared to other types of questions. This can add to the stress and anxiety of students, especially during an exam.
• Fear of Making Mistakes: Since Case Study questions involve applying concepts to real-world situations, students may fear making mistakes or getting the wrong answer. This fear may cause them to avoid attempting the question altogether.

In conclusion, students may fear Case Study questions for Class 10 Maths due to the application of concepts, limited practice, lengthy and complex scenarios, time pressure, and fear of making mistakes. Teachers can help alleviate these fears by providing ample practice opportunities, breaking down the scenarios into smaller parts, and encouraging students to attempt the questions.

Best Way to Approach Case Study Questions for Class 10 Maths

Here are some tips on how to approach Case Study questions for Class 10 Maths:

• Read the scenario carefully: The first step is to read the scenario carefully and identify the key information. Pay attention to the given values, units, and any other important details.
• Identify the mathematical concepts involved: Once you have read the scenario, identify the mathematical concepts that are involved. This will help you determine which formulas or equations to apply.
• Break down the scenario into smaller parts: Some Case Study questions may have lengthy and complex scenarios. To make it easier, try to break down the scenario into smaller parts and identify the specific information that is needed to solve each part.
• Solve the problem step by step: Once you have identified the key information and the mathematical concepts involved, start solving the problem step by step. Show all the calculations and equations used.
• Check your answers: After you have solved the problem, check your answers to ensure that they are accurate and relevant to the scenario given. If possible, try to cross-check your answer using a different approach or formula.
• Practice, Practice, Practice: The more you practice Case Study questions, the more familiar you will become with the format and the types of scenarios presented. This will help you develop confidence and improve your performance.

In conclusion, approaching Case Study questions for Class 10 Maths involves careful reading of the scenario, identifying the mathematical concepts involved, breaking down the problem into smaller parts, solving the problem step by step, checking the answers, and practicing regularly.

Topics Covered in CBSE Class 10 Maths

Here are the topics covered in CBSE Class 10 Maths:

• Real Numbers: Euclid’s division lemma, HCF and LCM, irrational numbers, decimal representation of rational numbers, and the relationship between roots and coefficients of a quadratic equation.
• Polynomials: Zeros of a polynomial, relationship between zeros and coefficients of a polynomial, division algorithm for polynomials, and factorization of polynomials.
• Pair of Linear Equations in Two Variables: Graphical method of solution, algebraic methods of solution, and word problems based on linear equations.
• Quadratic Equations: Standard form of a quadratic equation, solutions of a quadratic equation by factorization and by using the quadratic formula, relationship between roots and coefficients, and nature of roots.
• Arithmetic Progressions: nth term of an AP, sum of first n terms of an AP, and word problems based on arithmetic progressions.
• Triangles: Properties of triangles, congruence of triangles, criteria for similarity of triangles, and Pythagoras theorem.
• Coordinate Geometry: Distance formula, section formula, area of a triangle, and equation of a line in different forms.
• Introduction to Trigonometry: Trigonometric ratios, trigonometric ratios of complementary angles, and word problems based on trigonometry.
• Some Applications of Trigonometry: Heights and distances.
• Circles: Tangent to a circle, number of tangents from a point on a circle, and chord properties.
• Constructions: Construction of bisectors of line segments and angles, construction of a triangle similar to a given triangle, and construction of a triangle of given perimeter and base angles.
• Areas Related to Circles: Areas of sectors and segments of a circle.
• Surface Areas and Volumes: Surface areas and volumes of spheres, cones, cylinders, and cuboids.

In conclusion, CBSE Class 10 Maths covers a wide range of topics including real numbers, polynomials, linear equations, quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry, circles, constructions, areas related to circles, and surface areas and volumes.

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