Angles of elevation to an airplane are measured from the top and the base of a building that is 40 m tall. The angle from the top of the building is 37°, and the angle from the base of the building is 40°. Find the altitude of the airplane. (Round your answer to two decimal places.)

Answer 1

draw a diagram.

seen from the plane, the top and bottom of the building subtend an angle of 3°

using the law of sines, the distance from the top of the building to the plane can be found by

40/sin3° = d/sin50°
d = 585.48 m

(h-40)/d = sin37°
h = 392.35 m