Final answer:
To find the angle of elevation for the parking garage ramps, we use the tangent function where the opposite side is the height between floors (10 feet) and the adjacent side is the length of the ramp (75 feet). Arketing this ratio yields an angle of approximately 7.6 degrees.
Step-by-step explanation:
The subject of the question is Mathematics, and we're solving a trigonometry problem related to determining the angle of elevation of a ramp. To find the angle of elevation for the parking garage ramps Bill is designing, we use right-angle trigonometry since the ramps form a right-angle triangle with the ground and the vertical distance between the floors. The vertical distance between the floors is 10 feet, and the ramp itself is 75 feet long. We can use the tangent function to find the angle:
Tan(\(\theta\)) = opposite/adjacent
In this problem, opposite is the height of the floors, which is 10 feet, and adjacent is the length of the ramp, which is 75 feet:
Tan(\(\theta\)) = 10/75
Next, we take the arctangent (inverse tangent) of 10/75 to find \(\theta\):
\(\theta\) = Arctan(10/75)
After calculating this using a calculator set to degree mode, we get:
\(\theta\) \(\approx\) 7.6 degrees
Therefore, the angle of elevation for the ramps is approximately 7.6 degrees.