Question

The diagram below shows a student using a clinometer to measure the height of a flagpole. When the student stands 40 feet away from its base and the clinometer is exactly 5 feet above the ground, the clinometer shows a 35° angle of elevation to the top of the pole. What is the approximate height (h) of the flagpole?

Answer 1

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.