The angle of elevation of a stationary cloud from a point 25 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. What is the height of the cloud above the lake-level?

A tower subtends an angle α on the same level as the foot of the tower and at a second point h metres above the first, the depression of the foot of the tower is β. Show that the height of the tower is h tan α cot β.

A man observes the angle of elevation of the top of the tower to be 45°. He walks towards it in a horizontal line through its base. On covering 20 m, the angle of elevation changes to 60°. Find the height of the tower correct to 2 significant figures.

From the top of a cliff 60 m high, the angles of depression of two boats are 30° and 60° respectively. Find the distance between the boats, when the boats are:

(i) on the same side of the cliff,

(ii) on the opposite sides of the cliff.