Question

An airplane 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 13 degrees and 22 degrees. How high is the airplane?

Answer 1

$tan 22° = (y/x) \\ y = x tan 22° = 0.404 x\\ tan 13° = {y / (x+5)}\\ 0.231 = { 0.404 x / (x+5)}\\ 0.231 (x+5) = 0.404 x\\ 0.231 x + 1.155 = 0.404 x\\ 1.155 = -0.231 x + 0.404 x\\ 1.155= 0.173 x\\ x = 6.676 miles\\ Hence Y = 0.404 x\\ Y = 0.404 (6.676)\\ Y = 2.697 miles\\$