Q. A tree breaks due to storm and the broken part bends, so that the tope of the tree touches the ground making an angle ${30}^o$ with it. The distance between the foot of the tree to the point where the top touches the ground is $8m$. Find the height of the tree.

Q. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle ${30}^o$ with it. The distance between the foot of the tree to the point where the top touches the ground is $8m$. Find the height of the tree.

Q. 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 ${60}^{\circ }$. 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 ${30}^{\circ }$ (see Fig.). Find the height of the tower and the width of the canal.

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

Q. 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 ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. (see Fig.). Find the distance travelled by the balloon during the interval.

Q. 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 ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the height of the tower.

Q. 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 ${30}^o$, 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 ${60}^o$. Find the time taken by the car to reach the foot of the tower from this point.

Q. 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 ${60}^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is ${45}^{\circ }$. Find the height of the pedestal.

Q. The angle of elevation of the top of a building from the foot of the tower is ${30}^{\circ }$ and the angle of elevation of the top of the tower from the foot of the building is ${60}^{\circ }$. If the tower is $50\text{m}$ high, find the height of the building.

Q.

Two poles of equal heights are standing opposite each other on either side of the road, which is $80m$ wide. From a point between them on the road, the angles of elevation of the top of the poles are ${60}^{\circ }$ and ${30}^{\circ }$, respectively. Find the height of the poles and the distances of the point from the poles.

Q. 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.

Q. The angle of elevation of the top of a tower from a point on the ground, which is $30\text{m}$ away from the foot of the tower, is ${30}^{\circ }$. Find the height of the tower.

Q. From the top of a $7$ m high building, the angle of elevation of the top of a cable tower is ${60}^{\circ }$ and the angle of depression of its foot is ${45}^{\circ }$. Determine the height of the tower.

Q. A kite is flying at a height of $60m$ 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 ${60}^{\circ }$. Find the length of the string, assuming that there is no slack in the string.

Q. 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 ${30}^{\circ }$ to ${60}^{\circ }$ as he walks towards the building. Find the distance he walked towards the building.

Q.

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 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?