From the top of a cliff 100 m high, the angles of depression of two boats on the same side of the cliff are 45° and 30°. Find the distance between the two boats. (Take √3 = 1.732)

An aeroplane flying horizontally at a height of 3000 m is observed at an angle of elevation of 60°. After 15 seconds the angle is 30°. Find the speed of the aeroplane in km/h.

A boy 1.5 m tall stands 20 m from a tree and finds the angle of elevation of its top to be 30°. Find the height of the tree.

A tower is 100 m high. Find the angle of elevation of its top from a point 100√3 m from its foot.

From the top of a cliff 80 m high, the angles of depression of two boats in line with the foot of the cliff are 45° and 30°. Find the distance between the boats.

The angles of elevation of the top of a tower from two points on the same side of it and in line with its foot are 30° and 60°. If the points are 40 m apart, find the height of the tower.

A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. How high up the wall does it reach, and how far is its foot from the wall?