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 . From a point 1500 feet closer to the mountain along the plain, they find that the angle of elevation is .
How high (in feet) is the mountain?

Answer 1

draw the picture. Draw the triangles.

triangleOuter: set base to b. Heigth h, angle given, so tangent is given.
h=btanTheta1
TriangleInner: set base to b-1500, height h, angle tiven.

h=(b-1500)tanTheta2

solve for h.