Question

A contractor is tasked with constructing a ramp from the level ground to a loading door positioned 10 feet higher than the ground. According to the code, the angle of elevation must not exceed 7°. Solve the following:

a) What formula will you use to determine the length of the ramp with a 7° angle of elevation? Provide the formula needed to calculate the length of the ramp, rounding to the nearest hundredth.

b) Which formula will you employ to determine the horizontal distance along the ground from the base of the door where the ramp construction should commence? State the formula required to find this distance, rounding to the nearest hundredth.

Answer 1

The formula to calculate the length of the ramp with a 7° angle of elevation is ℎ = /(), and the formula to calculate the horizontal distance along the ground from the base of the door where the ramp construction should commence is ℎ = ℎ * ().

Step-by-step explanation:

To determine the length of the ramp with a 7° angle of elevation, you can use the formula:
Length of ramp = height / sin(angle)

Where:
- Height is the vertical distance between the ground and the loading door (in this case, 10 feet)
- Angle is the angle of elevation (in this case, 7°)

Substituting the values into the formula:

Length of ramp = 10 / sin(7°) ≈ 84.11 feet

To determine the horizontal distance along the ground from the base of the door where the ramp construction should commence, you can use the formula:
Horizontal distance = length of ramp * cos(angle)

Substituting the values into the formula:

Horizontal distance = 84.11 * cos(7°) ≈ 83.58 feet