The angle of elevation of a church-spire at some point in the plane is 45°. On proceeding 30 m towards the church, the angle of elevation becomes 60°. Find the height of the church-spire.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and that of the top of the flagstaff is β. Prove that the height of the h tan a tower is .

From a point on the level ground, the angle of elevation of the top of a tower is 30°. On proceeding 30 m towards the tower the angle of elevation becomes 60°. Find the height of the tower.

The pilot of helicopter at an altitude of 1000 m sees two aeroplanes, one on his left and the other on his right at the same height and finds their angles of depression as 45° and 60°. Find the distance between the two aeroplanes.

As observed from the top of a 100 m tall light house, the angles of depression of two ships approaching it are 30° and 45°. If one ship is directly behind the other, find the distance between the two ships.