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.

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.

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.

A straight highway leads to the foot of a 50 m tall tower. From the top of the tower, the angles of depression of two cars on the highway are 30° and 60°. What is the distance between the two cars and how far is each car from 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.