An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

Answer 1

Draw a diagram. On the ground, mark the points
Q directly beneath the plane
R directly beneath the line of flight, in the line of sight.

Then

x^2 = OR^2 + RQ^2 + 21000^2

I think something is missing. We only have a vertical distance, and an angle flat on the ground. Without knowing some of the distances from O to the flight line in the air or on the ground, we're stuck.

Or, maybe I have misinterpreted the language. If so, fix th drawing and solve for the distances involved.

Answer 2

I just see a right-angled triangle where

sin55° = 21000/x
x = 21000/sin55 = appr 25,636.3