You are standing 137 feet away from the base of a building and your clinometer measures 28° when it’s looking at the top of the building. (This angle is the one between the ground and the top of the building). Please calculate the height of the building.

The correct answer is the flagpole is 33 feet high.

Explanation:

Please refer to the attached picture.

We know:

CD = 40 feet

AC = 5 feet

∠BDC = α = 35°

Using trigonometry, we know that the definition of the tangent of an angle is the ratio between the opposite side and the adjacent side, therefore:

tan α = BC / CD

Solving for BC:

BC = CD · tan α

     = 40 · tan (35)

     = 28 feet

In order to find the height of the flagpole, we need to add the distance of the clinometer from the ground:

AB = BC + AC

     = 28 + 5

     = 33

Hence, the flagpole is 33 feet high.