Question

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 from the building, what is the height of the building. Round your answer to the nearest tenth.

Answer 1

The height of the building is 35.3 feet

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