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.

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

john earns $14.00 for two hours of work.

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130