NCERT Solutions for Class 10 Maths Unit 9

Some Applications of Trigonometry Class 10

Unit 9 Some Applications of Trigonometry Exercise 9.1 Solutions

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Exercise 9.1 : Solutions of Questions on Page Number : 203

Q1 :  

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 °.


Answer :

It can be observed from the figure that AB is the pole.

In ΔABC,

Therefore, the height of the pole is 10 m.

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Q2 :  

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.


Answer :

Let AC was the original tree. Due to storm, it was broken into two parts. The broken part is making 30° with the ground.

In ,

Height of tree = + BC

Hence, the height of the tree is.

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Q3 :  

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


Answer :

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Q4 :  

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.


Answer :

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Q5 :  

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.


Answer :

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Q6 :  

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.


Answer :

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Q7 :  

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.


Answer :

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Q8 :  

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 60° and from the same point the angle of elevation of the top of the pedestal is 45 °. Find the height of the pedestal.


Answer :

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Q9 :  

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.


Answer :

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Q10 :  

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 60° and 30º, respectively. Find the height of poles and the distance of the point from the poles.


Answer :

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Q11 :  

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 joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.


Answer :

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Q12 :  

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.


Answer :

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Q13 :  

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.


Answer :

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Q14 :  

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°. Find the distance travelled by the balloon during the interval.


Answer :

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Q15 :  

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 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.


Answer :

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Q16 :  

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.


Answer :

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<< Previous Chapter 8 : Introduction to Trigonometry Next Chapter 10 : Circles >>

Maths : CBSE NCERT Exercise Solutions for Class 10th for Some Applications of Trigonometry ( Exercise 9.1 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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