Question

A person whose eye level is 20 feet above the ground is looking at a building. The angle of elevation to the top of the building is 31º and the angle of depression to the bottom of the building is 24∘. What is the height (in feet) of the building? Round your answer to the nearest foot.

Answer 1

Distance of the person from the building (x)

tan 24 = 20/x => x = 20/tan 24 = 44.92 ft

The height of the building above the height of the person and the distance of the person from the building forms two legs of right angled triangle.

Therefore, if h is the height of the building, then;
tan 31 = (h-20)/44.92
h-20 = 44.92 tan 31
h = (44.92 tan 31) + 20 = 26.99 + 20 = 46.99 ft