Final answer:
The angle of inclination for a 9.0% grade is found by taking the inverse tangent of 0.09, which gives us an angle of approximately 5.1 degrees when rounded to the nearest tenth.
Step-by-step explanation:
To find the angle of inclination that corresponds to a 9.0% grade, we need to understand that the percent grade represents the tangent of the angle of inclination. The 9.0% grade means there is a rise of 9.0 feet for every 100 feet of horizontal distance. In mathematical terms, this can be expressed as tan(θ) = Δy / Δx, where θ is the angle of inclination, Δy is the rise, and Δx is the run. For a 9.0% grade, the tangent of the angle is 9/100, which is 0.09.
To find the angle, we must take the inverse tangent (arctan) of 0.09:
θ = arctan(0.09)
Using a calculator to find the inverse tangent, we get:
θ ≈ 5.1°
Therefore, the angle of inclination that corresponds to a 9.0% grade, when rounded to the nearest tenth, is approximately 5.1 degrees.