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

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45^o. Find the height of the tower PQ and the distance PX. 

173.

In Given figure, a tower AB is 20 m high and BC, its shadow on the ground, is m long. Find the sun's altitude.

The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the cloud from the surface of the water. 

As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [ Use √3= 1.732 ]

The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30^o. The distance of the car from the base of the tower (in m.) is

• 25√3

• 50√3

• 75√3

• 150