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riadik2000 [5.3K]
3 years ago
8

The diagram below shows a student using a clinometer to measure the height of a flagpole. When the student stands 40 feet away f

rom 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?

Mathematics
1 answer:
AVprozaik [17]3 years ago
5 0
The correct answer is the flagpole is <span>33 feet high</span>.

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 · <span>tan α
      = 40 </span>· 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.

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