Height and Distance Questions

The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is

The length of shadow of a tower is √3 times that of its length. The angle of elevation of the sun is

A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8√3 m from its foot and makes an angle of 30° with the horizontal. The height (in metre) of the post is

From the top of a platform 7 m high, the angle of elevation of a tower was 30 deg. If the platform was positioned 50√3 m away from the tower, how tall was the tower?

A pilot in an aeroplane at an altitude of 200 m observes two points lying on either side of a river. If the angles of depression of the two points be 45° and 60°, then the width of the river is

Two poles of the height 15 m and 20 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

If the length of the shadow of a vertical pole on the horizontal ground is √3 times its height, then the angle of elevation

From the top of a platform 5 m high, the angle of elevation of a tower was 30 deg. If the platform was positioned 40√3 m away from the tower, how tall was the tower?