Height and Distance Questions

From the top of a building, the angles of elevation and depression of top and bottom of a tower are 60 deg and 30 deg respectively. If the height of the building is 5m, then the height of the tower is

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

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

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

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

From the top of a platform, the angle of elevation of a tower was 30 deg. The tower was 45 mts high and the horizontal distance between the platform and the tower was 40√3 m. What was the height of the platform?

The angle of elevation of the top of a 36 m tall tower from the initial position of a person on the ground was 60 deg. She walked away in a manner that the foot of the tower, her initial position and the final position were all in the same straight line. The angle of elevation of the top of the tower from her final position was 30 deg. How much did she walk from her initial position?