Solve the problem.
-An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as 14° and 24°. How high is the airplane?
A) 2.03 mi
B) 2.83 mi
C) 1.21 mi
D) 4.76 mi

Question

Quizplus · Accepted Answer

The height of the airplane can be found using trigonometry, specifically the tangent of the angles of elevation. Let $ h $ be the height of the airplane, and $ x $ be the distance from the closer observer to the point directly below the airplane. The tangent of the angles gives two equations: $$ \tan(14^\circ) = \frac{h}{x} $$ and $$ \tan(24^\circ) = \frac{h}{5-x} $$. Solving these equations simultaneously, we find that $ h $ is approximately 2.83 miles.

Solve the Problem. -An Airplane Is Sighted at the Same Time by Two