Question

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 24. From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 27.
How high (in feet) is the mountain?

Answer 1

Make a sideview sketch
you should have 2 triangles, one right-angled containing the height and a scalene triangle with angles 24° , 153° (the supplement of 27°) and 3°
the side opposite the 3° angle is 1000
by let the side opposite the 24° be x, (also the hypotenuse of the right-angled triangle)

x/sin24 = 1000/sin3
x = 1000sin24/sin3

let the height of the mountain be h
sin 27 = h/x
h = x sin27 = (1000sin24/sin3)(sin27)
= 3528.25