precal :-/
An airplane is sighted at the same time by two ground observers who are 3 miles apart and both directly west of the airplane. They report the angles of elevation as 13 degrees and 20 degrees. How high is the airplane?

Question

precal  :-/
An airplane is sighted at the same time by two ground observers who are 3 miles apart and both directly west of the airplane. They report the angles of elevation as 13 degrees and 20 degrees. How high is the airplane?

anonymous · Answer

Make two right triangles, one with base =x and the other with base= 3+x. The nearer one has the 20o angle to the plane. The farther one has the 13o angle

height = x tan (20o)=.364 x
height = (x + 3) tan (13o) = .231 (x+3)

set height = height to get x
substitute x into one of the equations to get height.