What percentage of grade corresponds to a 45-degree angle?

The correct answer is based on the relationship between the angle of inclination and the percentage of grade. A 45-degree angle corresponds to a rise equal to the run, meaning that for every unit of horizontal distance, there is an equal unit of vertical rise.

To convert an angle to a percentage grade, you can use the tangent function from trigonometry, which in the case of a 45-degree angle has a tangent value of 1. This indicates that the grade is 1:1, or 100 percent. In terms of practical terms, this means for every 1 foot of horizontal distance traveled, the elevation changes by 1 foot, leading directly to a 100 percent slope.

The other choices reflect different angles of slope that do not correspond to a 45-degree angle. For instance, a 50 percent grade corresponds to a much shallower angle, while a 75 percent grade would be steeper, but not as steep as represented by 100 percent. Therefore, the identification of a 45-degree angle specifically correlates directly with a 100 percent grade.