A surveyor stands 75 feet from a building. He measures the angle of elevation to the top of the building at 67.5°. How tall is the building?

1694 ft

Step-by-step explanation:

The adjacent side of this right triangle is 75 feet in length, and the two given angles are 90 degrees and 67.5 degrees. Since the adjacent side is given and the opposite side is what we are looking for we can use

tan(x) = opposite/adjacent          insert the given information into the equation

tan(67.5) = opposite / 75ft           multiply both sides of the equation by 75

tan(67.5)*75 = opposite              leaving us with the target variable

once you plug that equation into a calculator you get 1694 as your nearest whole answer.

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