Question Type 3: Applying values of elevation and depression Exercises

An airplane is flying horizontally at 3000 m altitude. An observer on the ground measures the angle of depression to the plane as 15°. How far horizontally is the plane from the observer?

A 50 m tall tower casts a shadow on level ground such that the angle of elevation of the sun is 37°. Calculate the length of the shadow.

From the top of a cliff 80 m high, the angle of depression to a ship at sea is 25°. Find the horizontal distance between the cliff base and the ship.

From the top of a lighthouse 60 m above sea level, the angle of depression to a boat is 12°. How far is the boat from the lighthouse horizontally?

A man 2 m tall stands 30 m from a building. The angle of elevation to the top of the building from his eyes (1.6 m above ground) is 50°. Find the building’s height.

A balloon is rising vertically. From a point on the ground 100 m away, the angle of elevation is 30°. After it rises 50 m more, the angle is 45°. Find its initial height.

An observer moves towards a tower by 40 m, and the angle of elevation changes from 20° to 40°. Find the height of the tower.

An observer 1.5 m tall sees the top of a wall at an angle of elevation of 45°. If the observer’s eyes are 1 m above ground level, find the height of the wall.

A surveyor measures the angle of elevation to the top of a hill at two points 200 m apart on level ground; the angles are 25° and 32°. Find the height of the hill above the lower point.

A tower stands on level ground. From a point A, the angle of elevation to the top is 60°, and from a point B 20 m closer to the tower along the line of sight, the angle is 75°. Find the height of the tower.

From a point A, the angle of depression to the foot of a mountain is 35°; from a point B 150 m lower on the slope (vertically), the angle is 20°. Find the height of the mountain above point A.