Height and Distance Questions

A balloon is connected to a meteorological station by a cable of length 130 m, inclined at 60 deg to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in cable.

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

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 an aeroplane from a point on the ground is 60 deg. After flying for 30 seconds, the angle of elevation changes to 30 deg. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?