The angle of elevation of the top of a tower from a point on the ground is 30°. After walking 30 m towards the tower, the angle of elevation becomes 60°. What is the height of the tower?

When the altitude of the Sun increases from 30° to 45°, the length of the shadow of a palm tree decreases by 12 m. Find the length of the palm tree.

A tall tree stands vertically on a bank of a river. At the point on the other bank directly opposite the tree, the angle of elevation of the top of the tree is 60°. At a point 20 m behind this point on the same bank, the angle of elevation of the top of the tree is 30°. Find the height of the tree and the width of the river.

At a point P on the ground, the angles of elevation of the top of a 10 m tall building, and of a helicopter covering some distance over the top of the building, are 30° and 60° respectively. Find the height of the helicopter above the ground.

From an aeroplane, the angles of depression of two ships in a river on left and right of it are 60° and 45° respectively. If the distance between the two ships is 100m, find the height of the aeroplane.