Word problem

Question

AN airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation at 11 degrees and 20 degrees. How high is the airplane? round to the nearest hundredth of a mile.

Answer 1

Draw and label a diagram. A is closer to the point below the plane.

h represent the height of the plane

tan 20° = h/x ⇒ x tan 20° = h

tan 11° = h/(x + 2) ⇒ (x + 2)tan 11° = h

 

x tan 20° = (x + 2)tan 11°

 

Solve for x then substitute into either equation to calculate h.