Exercise 6.6 — Class 9 Mathematics Solutions

The angle of elevation of the top of a flag post from a point on the ground level $40$ m away from the flag post is ${60}^{\circ }$. Find the height of the post.

An isosceles triangle has a vertical angle of ${120}^{\circ }$ and a base $10$ cm long. Find the length of its altitude.

A tree is $72$ m high. Find the angle of elevation of its top from a point $100$ m away on the ground level.

A ladder makes an angle of ${60}^{\circ }$ with the ground and reaches a height of $10$ m along the wall. Find the length of the ladder.

A light house tower is $150$ m high from the sea level. The angle of depression from the top of the tower to a ship is ${60}^{\circ }$. Find the distance between the ship and the tower.

The measure of the angle of elevation of the top of a pole is ${15}^{\circ }$ from a point on the ground. On walking $100$ m towards the pole, the measure of the angle is found to be ${30}^{\circ }$. Find the height of the pole.

Find the measure of the angle of elevation of the Sun if a tower $300$ m high casts a shadow $450$ m long.

The measure of the angle of elevation of the top of a cliff is ${25}^{\circ }$. On walking $100$ metres towards the cliff, the measure of the angle of elevation of the top is ${45}^{\circ }$. Find the height of the cliff.

From the top of a hill $300$ m high, the measure of the angle of depression of a point on the nearer shore of the river is ${70}^{\circ }$, and the measure of the angle of depression of a point directly across the river (on the far shore) is ${50}^{\circ }$. Find the width of the river. How far is the river from the foot of the hill?

A kite has $120$ m of string attached to it when at an elevation of ${50}^{\circ }$. How far is it above the hand holding it? (Assume that the string is tight.)