Question

A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet and the child’s eyes are located 8,200 feet away from a point on the ground directly beneath the plane, what is the angle of elevation for the child’s line of sight to the plane?

Answer 1

about 76.2°

Explanation:

The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.

Tan = Opposite/Adjacent

tan(angle) = (33,500/8,200)

angle = arctan (335/82) ≈ 76.246°

The angle of elevation is about 76.2°.