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#### Question

The tops of two towers of height *x *and *y,* standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find *x*, *y*.

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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.

A ladder makes an angle of 60° with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is:

(A) `4/sqrt3`

(B) `4sqrt3`

(C) `2sqrt2`

(D)4

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30˚. The angle of depression of the reflection of the cloud in the lake, at A is 60˚.

Find the distance of the cloud from A.

A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30º and that of the top of the flagstaff is 45º. Find the height of the tower.

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.