A mountain peak C is 4130 ft. Above sea level, and from C the angle of elevation of a second peak B is 5.0°. An aviator at A directly over peak C finds that angle CAB is 43.8° when his altimeter shows that he is 8460 ft. Above sea level. Find the height of peak B.

Answer 1

draw a diagram. You can see that if B and C are separated by a horizontal distance of x ft, then

x/(8460-h) = tan43.8°
(4130-h)/x = tan5°

eliminating x, we get

(8460-h)tan43.8° = (4130-h)/tan5°
h = 3734