A 12 m high tree breaks due to wind such that its top touches the ground and makes an angle of 60° with the ground. Find at what height from the earth has the tree broken by the wind (√3 = 1.732)?

From a point of the bridge of a river the angles of depression of the opposite banks of the river are 30° and 45°. If the bridge is at a height of 4m from the banks, then find the width of the river.

A man is standing on the deck of a ship, which is 10 m above the water level. If he observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°, then find the distance of the hill from the ship and the height of the hill.

A highway passes through the foot of a tower. A man observes a car at an angle of depression of 30° from the top of the tower. That car is approaching the foot of the tower. Six seconds later, the angle of depression of the car becomes 60°. In what time will the car pass through the foot of the tower?

The angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are supplementary. Prove that the height of the tower is 6m.