How high (in feet) is the mountain?

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 and label a diagram.

A is the first observation point

B is the second observation point

C is the base of the mountain

h is the height of the mountain

cot 30° = BC / h

h cot 30° = BC

cot 26° = (1500 + BC) / h

h cot 26° = 1500 + BC

h cot 26° - 1500 = BC

h cot 30° = h cot 26° - 1500

Can you solve for h and answer?