Question

A plane is flying at an altitude of 32,000 feet. The distance between the plane and a radio tower on the ground is 50,000 feet. What is the angle of depression between the plane and radio tower

Answer 1

This is a basic trigonometry problem. Essentially, you could put a triangle in where the plane to the base of the tower is the hypotenuse, the tower to the height of the plane is a vertical leg (straight up from the tower) and the line can be redrawn horizontally to the plane. The height of the vertical leg is 30000 and your hypotenuse (the distance from plane to tower) is 50000 feet. Your angle of depression is the angle between the horizontal line and the hypotenuse. You can thus use \[\sin (\theta) = \frac{ opposite }{ hypotenuse }\] Solving for theta using arcsin will solve the problem.