A man at ground level measures the angle of elevation to the top of a building to be 67°. If at this point, he is 15 feet away f
rom the building, what is the height of the building. Round your answer to the nearest tenth.
1 answer:
Answer:
The height of the building is 35.3 feet
Step-by-step explanation:
To find the height of the building, we will follow the steps below:
Using trigonometric ratio to solve;
SOH CAH TOA
Sin Ф = opposite / hypotenuse
cosФ = adjacent /hypotenuse
tanФ=opposite / adjacent
From the diagram below, we have our opposite = h, adjacent =15 feet and Ф = 67°
where h is the height of the building
The best formula to use is;
tanФ= opposite/adjacent
tan 67° = h/15
Multiply both-side of the equation by 15
15 ×tan 67° = 15× h/15
35.33778549 = h
h≈35.3 feet to the nearest tenth
The height of the building is 35.3 feet
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