Heights And Distances

A bridge over a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, find the width of the river.

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°. Find the tower height.

A statue 1.6 m tall stands on a pedestal. From a point, the elevation of the top of statue is 60° and pedestal top is 45°. Find pedestal height.

The shadow of a tower is found to be 40 m longer when the sun's altitude is 30° than when it is 60°. Find the tower height.

A TV tower stands vertically on a bank of a canal. From a point 20 m away from the bank, the angle of elevation is 30°. From the bank, it is 60°. Find the canal width.

An observer 1.5 m tall is 20.5 m away from a tower 22 m high. What is the angle of elevation?

Two ships are on the same side of a lighthouse. The angles of depression from the 100 m lighthouse are 30° and 45°. Find the distance between ships.

A flagstaff of 5 m height stands on a tower. From ground, elevations of top and bottom of flagstaff are 60° and 45°. Tower height?

If the height of a pole is increased by 10%, and the angle of elevation remains 45°, the shadow length:

From a point P on the ground, the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top. The angle of elevation of the top of the flag is 45°. Find the length of the flag.

Angle of elevation of a cloud from a point 60 m above a lake is 30° and depression of its reflection in lake is 60°. Height of cloud?

A person standing on the bank of a river observes the angle of elevation of a tree on the opposite bank as 60°. When he moves 40 m away, it becomes 30°. Width of river?

A vertical pole and a tower are on the same ground. The angle of elevation of the top of the tower from the top and bottom of the pole are 30° and 60° respectively. If tower is 90 m, pole height is:

A plane flying at 3000 m passes vertically above another plane at an instant when elevations of the two planes from the same point are 60° and 45°. Distance between planes?

The angles of elevation of the top of a tower from two points on the ground at distances 4 m and 9 m from the base are complementary. Tower height?

A 10 m long pole is broken by wind. The top touches the ground at 30° with ground. Find the height of the break.

The ratio of height of a tower and distance of point is √3:1. Elevation is:

Two poles 12 m and 18 m high stand vertically. If the string connecting their tops makes 30° with horizontal, find distance between them.

From a lighthouse 100 m high, the angles of depression of two ships are 30° and 60°. If ships are on opposite sides, find distance between them.

Angle of elevation of a tower from a point is 45°. Moving 10 m away, it becomes 30°. Height?