CBSE Class 10 Maths 2024-25: Chapter 9 Some Applications of Trigonometry Competency-Based Questions with Answers; Download Free PDF

As the CBSE Class 10 board exams get closer, it’s important for students to understand the new exam pattern. Starting in the 2024-25 school year, CBSE will include 50% more competency-based questions. These questions will be both multiple choice and written, focusing on how to use what students have learned in real-life situations.

This article explores Chapter 9 Some Applications of Trigonometry. It highlights key competency-based questions and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 9 Some Applications of Trigonometry

Competency-based questions are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as case studies, true-false questions, gap-filling tasks, and long or short answer questions.

Competency-based questions in Chapter 9: Some Applications of Trigonometry go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 9: Some Applications of Trigonometry Important Competency-Based Questions

Multiple Choice Questions

Q.1 The angle of elevation of the top of a tower from point A on the ground is 30°. The tower is 50 m high.

Approximately how far is point A from the foot of the tower?

( Note: Take √3 as 1.73.)

1. 28.90 m
2. 50 m
3. 86.50 m
4. 100 m

Answer. (3)

Q.2 At a particular time of the day, Shreya noticed that the length of her shadow was equal to her height.

Which of these is the measure of the angle of elevation of the sun from her head?

1. 30°
2. 45°
3. 60°
4. 90°

Answer. (2)

Q.3 A kite is tied to a point on the ground. The length of the string between the kite and the point on the ground is 80 m. The string makes an angle θ with the ground such that tan θ = 60°. What is the height of the kite above the ground?

1. 20√3 m
2. 40 m
3. 40√3 m
4. 80√3 m

Answer. (3)

Q.4 A wheelchair ramp needs to be built from the ground to a door that is 2 m above the ground. If the angle of inclination for the ramp is 30 ° , what should be the length of the ramp?

1. 2√3
2. 2 m
3. 4/√3 m
4. 4 m

Answer. (4)

Q.5 From the top of a hill, it is observed that the angle of depression of the top of a tree and its foot are 45° and 60° respectively. The height of the tree is 20 m.

What is the height of the hill?

(Note: The base of the hill and the tree are on the same level.)

1. 10(√3 + 1) m
2. 20 + 20(√3 + 1) m
3. 20 + 10(√3 + 1) m
4. 20 - 10(√3 + 1)) m

Answer. (3)

Q.6 A 10 m tall pole casts a shadow of 15 m when the sun is at a certain inclination. At the same time, a nearby building casts a shadow of 25 m.

How tall is the building?

1. 16.67 m
2. 20 m
3. 37.5 m
4. (cannot be determined with the given information.)

Answer. (1)

Q.7 A pole, whose height is h units, is standing straight up on the ground. The top of the pole subtends an angle β with a specific point on the ground.

Which of these gives the distance from the bottom of the pole to the point on the ground?

Answer. (3)

Q.8 A helicopter moving linearly with a uniform speed at an altitude of 600 m is observed at an angle of elevation of 45°. After 15 seconds, the angle of elevation is observed to be 30°. Which of these is the speed of the helicopter in metres per second?

1. 40√3
2. 40(√3 - 1)
3. 40(√3 + 1)
4. 600(√3 - 1)

Answer. (2)

Free Response Questions

Q.9 A car is driving up a hill inclined at 30°. It covers a distance of 500 m along the hill.

i) Draw a figure to represent the situation.

ii) Find the vertical height the car gained during the journey. Show your work.

Answer. i) Draws a figure representing the given information. The figure may look as follows:

Q10. A ladder leans against a vertical wall. The foot of the ladder is 8 m away from the wall at an inclination of 60° from the ground.

Find the length of the ladder. Show your work

Answer. Uses the trigonometric ratio to write:

Q.11 An Olympic shooter is aiming a gun at a target from the edge of a cliff such that the gun is 270 m above the ground. The angle of depression of the target from the gun is 30°.

What is the shortest distance between the gun and the target?

Answer.

Q.12 A boy was flying a remote-controlled helicopter. The helicopter was observed at an altitude of 50√3 metres when it was directly overhead the boy.

The helicopter flew 50 metres horizontally making an angle of depression, θ from the boy. Draw a rough diagram to represent this situation and find the value of θ. Show your work.

Answer. Draws a rough diagram to represent the situation. The figure may look as follows:

Case Study

Answer the questions based on the given information.

Arun, Nikhil and Suman visited a park that had many recreational activities for children including slides and kites for them to enjoy. Arun found the slide interesting and he went to try it out. Nikhil and Suman went for kite flying. At a given instant, the position of Nikhil's kite and its angle of elevation from the ground is as shown assuming the string of kite forms a straight line without any snags.

Q.13 Find the tangent of the angle of depression from the top of the slide to the ground.

Answer. Uses Pythagoras' theorem to find the distance between the foot of the slide and the 1 ladder as:

Q.14 What is the height of Nikhil's kite from the ground at the given instant?

( Note: Nikhil's height is to be ignored. )

Answer. Uses the sine ratio and substitutes the values to write:

Solves the above equation to find height of kite as 54 m.

Q.15 Nikhil's kite got stuck on the roof of a neighbouring building. Suman saw this and used a ladder to climb up the roof. The ladder was 25 m long and was positioned 7m away from the base of the building. As Suman started to climb, the ladder slipped by 4 m from point (a) to (b) as shown below.

(Note: The figure is not to scale.)

Find the distance by which the foot of the ladder slid along the ground. Show your work.

Answer. Draws a rough labelled diagram. The labelled diagram may look as follows:

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