A helicopter hovers at an altitude that is 2000 feet above a mountain peak of altitude 5280 feet. A second taller peak, is viewed from both the mountain top and the helicopter. From the helicopter, the angle of depression is 43° 55'. From the mountain top, the angle of elevation is 18° 40'. Find:

Question

a) The distance from peak to peak.
b) Altitude of the peak of the taller mountain.

Answer 1

If the distance is x and the other peak has height h, note that

(7280-h)/x = tan43°55'
(h-5280)/x = tan18°40'

Now you can easily find x and h.