From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are `30^@` and `45^@`, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

From the top of a hill 200 m high, the angles of depression of the top and the bottom of a pillar are 30^@ and 60^@ respectively. Find the height of the pillar and its distance from the hill.

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road the angles of elevation of the top of the poles are 60^@ and 30^@ , respectively. Find the height of the poles and the distances of the point from the poles.

From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45^@ and 60^@ respectively. Find the height of the tower.

From a window (h metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are theta and phi respectively. Show that the height of theopposite house is h (1 + tan theta cot phi) .

From a building 60 metres high the angle of depression of the top and bottom of lamppost are 30^@ and 60^@ respectively. Find the distance between lamp post and building. Also find the difference of height between building and lamp post.

An aeroplane, when 3000 m high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 60^@ and 45^@ respectively. Find the vertical distance between the two aeroplanes.

On a horizontal plane there is a vertical tower with a flag on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60^@ and 30^@ respectively. Find the height of the tower and flag pole mounted on it.

As observed from the top of a 75 m high lighthouse 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 lighthouse, find the distance between the two ships.

From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be alpha and beta (alpha >beta) . If the distance between the objects is 'p' metres, show that the height 'h' of the tower is given by h=frac(p tan alpha tan beta)(tan alpha-tan beta) also determine the height of the tower, if p=50 m , alpha=60^@, beta=30^@

From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30^@ . The angle of elevation to the top of a water tank (On the top of the tower) is 45^@ . Find the height of the tower and the depth of the tank.