What is the altitude of the plane?

Question

A plane approaches an airport runway. The runway is 9000ft long. The pilot sights the start of the runaway at an 18.8° angle of depression, and the end of the runway at a 17.5° angle of depression. What is the altitude of the plane?

Answer 1

Draw and label a diagram.

a represents the altitude of the plane

x represents the ground distance to the start of the runway

a / x = tan 18.8°

a = x tan 18.8°

a / tan 18.8° = x

a / (x + 9000) = tan 17.5°

a = (x + 9000) tan 17.5°

a = x tan 17.5° + 9000 tan 17.5°

a - 9000 tan 17.5° = x tan 17.5°

(a - 9000 tan 17.5°) / tan 17.5° = x

a / tan 18.8° = (a - 9000 tan 17.5°) / tan 17.5°

Can you solve for a and answer?