Problem

A road has a grade of 12%. What is the angle of this grade in degrees?

Answer

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Answer

So, the calculation is: arctan⁡(0.12)×180π

Steps

Step 1 ：First, we need to understand that percent grade is the ratio of the vertical change to the horizontal change, so it's essentially a tangent of the angle we're looking for.

Step 2 ：So, to find the angle, we need to take the inverse tangent (arctan) of the percent grade (which should be converted to decimal form first). In this case, we have: arctan⁡(0.12).

Step 3 ：However, the output of the arctan function is usually in radians, so we need to convert it to degrees. The conversion is done by multiplying the result by 180π.

Step 4 ：So, the calculation is: arctan⁡(0.12)×180π

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