Question

A contractor needs to build a ramp from the level ground up to a loading door that is 10 feet higher than the ground. By code, the angle of elevation can be no greater than 7°.

a) How long must the ramp be if a 7° angle of elevation is used? Round to the nearest hundredth.
b) How far along the ground from the base of the door should the contractor begin building the ramp? Round to the nearest hundredth.

Answer 1

Using trigonometric functions with the given 7° angle of elevation, the ramp length is calculated to be approximately 81.68 feet, and the ground distance from the base of the door to start the ramp is approximately 81.32 feet.

Step-by-step explanation:

To determine the length of the ramp at a 7° angle of elevation, we use trigonometric functions. Specifically, the cosine of the angle of elevation, which is the adjacent side (the ground length) over the hypotenuse (the ramp length), is needed here. We have the opposite side, which is the rise of the ramp (10 feet).

Using the cosine function:

• cos(7°) = adjacent/hypotenuse
• cos(7°) = ground length/ramp length

Since the rise is 10 feet, we can use the tangent function to find the ground length:

• tan(7°) = opposite/adjacent
• tan(7°) = 10/ground length

After calculating, we find:

• The ramp length needs to be approximately 81.68 feet.
• The ground distance from the base of the door to start the ramp is approximately 81.32 feet.