Question

What is the angle of elevation if you are standing 400 ft. away from a building that is 950 ft. tall? Round your answer to the nearest tenth.

a) 65.5 degrees
b) 67.2 degrees
c) 69.8 degrees
d) 71.3 degrees

Answer 1

To determine the angle of elevation, one must use the arctangent of the building's height divided by the distance from the building. In this case, the correct answer is (b) 67.2 degrees when rounded to the nearest tenth.

Step-by-step explanation:

The question asks for the angle of elevation when standing 400 ft away from a 950 ft tall building. To find this angle, we use trigonometry, specifically the tangent function which is defined as the opposite side over the adjacent side in a right-angled triangle. In this scenario, the building height represents the opposite side of the triangle, and the distance from the building represents the adjacent side. Therefore, we compute the angle of elevation by taking the arctangent (inverse tangent) of the height of the building divided by the distance from the building:

angle of elevation = arctan(opposite/adjacent) = arctan(950/400).

Using a calculator to find the angle of elevation:

angle of elevation = arctan(950/400) ≈ arctan(2.375) ≈ 67.2 degrees.

Hence, the correct answer is (b) 67.2 degrees, rounded to the nearest tenth.