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.

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.

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?

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.

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?