Mathematics [4 marks sum]

The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 20°. Find the height of the tower.

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 40° and the angle of depression of its shadow in water of the lake is 65°. Find the height of the cloud from the surface of the water.

From the top of a tower 100 m high, a man observes two cars on opposite sides of the tower and in the same straight line with its base, with angles of depression 35° and 50°. Find the distance between the two cars.

A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in horizontal line through its base. On covering 60 m, the angle of elevation changed to 60°. Find the height of the building.