Question

A plane is flying at an altitude of 13,000 ft. The angle of depression from the plane to a control tower is 20°. The control tower is 150 feet high. What is the horizontal distance from the plane to the tower? Round to the nearest foot, and enter the number only

Answer 1

Explanation:

A diagram of the given information is shown below where the horizontal distance is denoted by the green arrows and the vertical distance is blue:

Note how the altitude of the plane is equal to the side opposite (opp) the angle of depression. Since the adjacent side (adj)is the horizontal distance of the plane from the airport, deriving the expression for the adjacent side and substituting the information in the tangent ratio gives: