Math Homework hlep, please

Question

The angle of elevation to the top of a very tall Building is found to be 8° from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the building. (Round your answer to the nearest foot.)

Answer 1

This problem can be modeled with a right triangle. The vertices are the spot on the ground 1 mile from the building, the bottom of the building, and the top of the building. The right angle is the bottom of the building, and we're told that the angle at the spot on the ground 1 mile from the building measures 8°.

 

Call the height of the building x. Since we have the measure of one leg and are looking for the measure of another (the height of the building), use tangent:

 

tan(8°) = opposite/adjacent

tan(8°) = x/1

tan(8°) = x

0.14054 = x

 

The building is 0.14054 miles tall. That's 0.14054 × 5280 feet/1 mile = 0.14054(5280) feet = 742.06 feet. To the nearest foot, the building is 742 feet tall.