What is the relationship between degrees of slope and percentage?

In the context of slope, the relationship between degrees and percentage is based on the tangent function from trigonometry, where the slope percentage is calculated as 100 times the tangent of the angle.

When a slope is measured in degrees, it indicates the steepness of the slope in relation to horizontal ground. For example, at 45 degrees, the tangent is 1, which translates to a 100% slope. This means that for every 100 units of horizontal distance, there is a vertical rise of 100 units, making it a 1:1 ratio. Thus, 45 degrees perfectly correlates to 100%, demonstrating the understanding that as the angle increases, the resultant percentage of slope also increases.

The correct answer, therefore, directly illustrates this fundamental principle of slope measurement in degrees compared to percentage, especially as the tangent of 45 degrees yields this distinct result of a 100% slope.