Question

. From the top of the 800-foot-tall Cartalk Tower, Tom sees a plane; the angle of elevation is 67°. At the
same instant, Ray, who is on the ground 1 mile from the building, notes that his angle of elevation to the
plane is 81° and that his angle of elevation to the top of Cartalk Tower is 8.6°. Assume Tom, Ray, and the
airplane are in a plane perpendicular to the ground. How high is the airplane?

I used right triangles and it gave me 9039.846ft but my teacher said that it was incorrect.

Answer 1

Let
x = distance from Ray to the point under the plane
h = height of plane

You can see from the diagram that

(h-800)/(5280+x) = tan67°
h/x = tan81°

Now just eliminate x and solve for h. I get 21,119
(c-800)/tan(67°) -5280 = c/tan(81°)