NCERT Solutions for Class 10 Mathematics Chapter 9 Some Applications of Trigonometry

NCERT Solutions for Class 10 Mathematics Chapter 9 - Some Applications of Trigonometry

Welcome to the Chapter 9 - Some Applications of Trigonometry, Class 10 Mathematics NCERT Solutions page. Here, we provide detailed question answers for Chapter 9 - Some Applications of Trigonometry. The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.

Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics Some Applications of Trigonometry and excel in their exams. By going through these Some Applications of Trigonometry question answers, you can strengthen your foundation and improve your performance in Class 10 Mathematics. Whether you’re revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.

Exercise 1

Q 1:

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° (see Fig. 9.11).

Let AB = hm be the height of pole and length of rope is 20 m tied from the

Top of tower AB and = 30^o

In right Δ ABC, we have

Q 10:

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.

Q 11:

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.

Q 12:

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.

Q 13:

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Q 14:

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.

Q 15:

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 with 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.

Q 16:

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

Let the height of tower AB = x m

Q 2:

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 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.

Q 3:

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, andis inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?

(i) For Children below age of 5 years

Height of slide = 1.5 m

Angle of inclination of slide = 30^o

(ii) For Children below age of 5 years

Height of slide = 3m

Angle of inclination of slide = 60^o

Draw figure for both cases:

In right Δ ABC, we have

Sin 30^o = AB / AC => 1/ 2 = 1.5 /AC [ sin30^o =1/2]

AC = 3m

In right Δ DEF, we have

Sin 60^o = DE /DF =>

DF =

Q 4:

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

Q 5:

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

Draw a figure according to given conditions,

Q 6:

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

Q 7:

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Let AB = x m be the height of transmission tower

BC = 20 m height of building (given)

Angle of elevation from top of tower = 60⁰

Angle of elevation from bottom of tower = 45^o

To find : height of tower i.e., AB

Q 8:

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Q 9:

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Frequently Asked Questions about Some Applications of Trigonometry - Class 10 Mathematics

- 1. How many questions are covered in Some Applications of Trigonometry solutions?
- All questions from Some Applications of Trigonometry are covered with detailed step-by-step solutions including exercise questions, additional questions, and examples.
- 2. Are the solutions for Some Applications of Trigonometry helpful for exam preparation?
- Yes, the solutions provide comprehensive explanations that help students understand concepts clearly and prepare effectively for both board and competitive exams.
- 3. Can I find solutions to all exercises in Some Applications of Trigonometry?
- Yes, we provide solutions to all exercises, examples, and additional questions from Some Applications of Trigonometry with detailed explanations.
- 4. How do these solutions help in understanding Some Applications of Trigonometry concepts?
- Our solutions break down complex problems into simple steps, provide clear explanations, and include relevant examples to help students grasp the concepts easily.
- 5. Are there any tips for studying Some Applications of Trigonometry effectively?
- Yes, practice regularly, understand the concepts before memorizing, solve additional problems, and refer to our step-by-step solutions for better understanding.

Exam Preparation Tips for Some Applications of Trigonometry

The Some Applications of Trigonometry is an important chapter of 10 Mathematics. This chapter’s important topics like Some Applications of Trigonometry are often featured in board exams. Practicing the question answers from this chapter will help you rank high in your board exams.

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