If a grade rises 86 feet over a horizontal distance of 277 feet, what is the percent of slope?

To find the percent of slope, you use the formula:

[

\text{Percent of slope} = \left( \frac{\text{Rise}}{\text{Run}} \right) \times 100

]

In this scenario, the rise is 86 feet and the run is 277 feet. Plugging these values into the formula gives:

[

\text{Percent of slope} = \left( \frac{86}{277} \right) \times 100

]

Calculating the fraction:

[

\frac{86}{277} \approx 0.3101

]

Now, multiply by 100 to convert it to a percentage:

[

0.3101 \times 100 \approx 31.01%

]

Rounding this value, we find that the percent of slope is approximately 31%. Therefore, the correct answer is indeed 31%, which matches the choice you selected. This calculation underscores the importance of knowing how to compute slope in a construction context, as slopes can affect drainage, structural stability, and other engineering considerations on a project.