NCERT Solution for Class 10 Mathematics Chapter 9 - Some Applications of Trigonometry RR ACADEMY MEERUT

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

Excercise 9.1

Question 1

Solution 1

Question 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 30o 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.

Solution 2

Let AC be the original tree and be the broken part which makes an angle of 30o with the ground.

Question 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, and is inclined at an angle of 30o to the ground, whereas for the elder children she wants to have a steep side at a height of 3 m, and inclined at an angle of 60o to the ground. What should be the length of the slide in each case?

Solution 3

In the two figures, AC and PR are the slides for younger and elder children respectively

Question 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 30o. Find the height of the tower.

Solution 4

Question 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 60o. Find the length of the string, assuming that there is no slack in the string.

Solution 5

Let A be the position of the kite and the string is tied to point C on ground.

Question 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 30o to 60o as he walks towards the building. Find the distance he walked towards the building.

Solution 6

Question 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 45o and 60o respectively. Find the height of the tower.

Solution 7

Let BC be the building, AB be the transmission tower, and D be the point on ground from where elevation angles are to be measured.

Question 8

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

Solution 8

Let AB be the statue, BC be the pedestal and D be the point on ground from where elevation angles are to be measured.

Question 9

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

Solution 9

Question 10

Two poles of equal heights are standing opposite each other an 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 60o and 30o, respectively. Find the height of poles and the distance of the point from the poles.

Solution 10

Question 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 60o. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30o. Find the height of the tower and the width of the canal.

Solution 11

Question 12

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60o and the angle of depression of its foot is 45o. Determine the height of the tower.

Solution 12

Question 13

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

Solution 13

Let AB be the lighthouse and the two ships be at point C and D respectively.

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Question 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 60o. After some time, the angle of elevation reduces to 30o. Find the distance travelled by the balloon during the interval.

Solution 14

Question 15

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car as an angle of depression of 30o, 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 60o. Find the time taken by the car to reach the foot of the tower from this point.

Solution 15

Let AB be the tower. C is the original position of the car which changes to D after six seconds.

Question 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.

Solution 16

Let AQ be the tower and R, S respectively be the points which are 4m, 9m away from base of tower.


As the height can not be negative, the height of the tower is 6 m.