Contents

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 10 |

Subject |
Maths |

Chapter |
Chapter 9 |

Chapter Name |
Some Applications of Trigonometry |

Exercise |
Ex 9.1 |

Number of Questions Solved |
16 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

### Chapter 9 Some Applications of Trigonometry Exercise 9.1

**Question 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°.**

**Solution:**

**Given:** length of the rope (AC) = 20 m, and ∠ACB = 30°

Let height AB of pole be h m.

Hence, height of the pole = 10 m

**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 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.**

**Solution:**

Let AB is the broken part which bends from the point B and touches the ground at D.

Given: ∠BDC = 30° and DC = 8 m

**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 30° to the ground, whereas for elder children, she wants to have a steep slide 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?**

**Solution:**

Let the length of slide for children below the age of 5 years be x m and length of the slide for elder children be y m.

**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 30°. Find the height of the tower.**

**Solution:**

**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 60°. Find the length of the string, assuming that there is no slack in the string.**

**Solution:**

**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 30° to 60° as he walks towards the building. Find the distance he walked towards the building.**

**Solution:**

**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 45° and 60° respectively. Find the height of the tower.**

**Solution:**

**Question 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.**

**Solution:**

**Given:** height of the statue = 1.6 m,

Let the height of the pedestal is h m and the point on the ground from the pedestal is x m away.

**Question 9.**

**The angle of elevation of the top of a building from the foot of a 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.**

**Solution:**

**Given:** height of the tower AB = 50 m,

Let h m be the height of the building

Then in right ∆ABQ,

**Question 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 distance of the point from the poles.**

**Solution:**

**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 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° (see the given figure). Find the height of the tower and the width of the CD and 20 m from pole AB.**

**Solution:**

Let the height of the tower AB be h m and x m be the width of the canal BC.

**Question 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.**

**Solution:**

**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 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.**

**Solution:**

Given: ∠ADB = 30°, ∠ACB = 45° and AB = 75 m**
**Let the distance between the ships be x m.

**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 60°. After sometime, the angle of elevation reduces to 30° (see figure). Find the distance travelled by the balloon during the interval.**

**Solution:**

**Question 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.**

**Solution:**

Let the height of the tower DC be h m and the speed of the car be x m/s.

Then the distance covered by the car in 6 s will be 6x m.

Also let the time taken by car to move from B to C be t s.

**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:**

Let h m be the height of tower and ∠CDB be θ.

Then ∠CAB = 90° – θ

In right ∆CBD,

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