The peak of a mountain is observed from the base and from the top of a tower 180 ft high. Find the height of the mountain above the base of the tower is the angles of elevation of the peak are 21 degree 35’ and 24 degree 48’

Answer 1

As usual, draw a diagram. It is clear that if the height of the mountain is h, and the tower is at a distance x from the mountain,

(h-180)/x = tan 21°35'
h/x = tan 24°48'

Eliminate x and you have

(h-180)/tan21°35' = h/tan24°48'

Now just solve for h