If a road has a 12% grade, what is the equivalent grade in degrees?

Step 1 ：Step 1: Understand that a 12% grade means that for every 100 units of distance travelled horizontally, you ascend 12 units vertically. This forms a right triangle where the hypotenuse is the road, the horizontal leg is 100 units, and the vertical leg is 12 units.

Step 2 ：Step 2: Use the tangent function to find the angle. The tangent of an angle in a right triangle is the length of the opposite side divided by the length of the adjacent side. So, $\tan (\theta )=\frac{12}{100}=0.12$

Step 3 ：Step 3: Use the inverse tangent function (also called the arctangent) to find the angle in radians. $\theta =\arctan (0.12)$

Step 4 ：Step 4: Convert the angle from radians to degrees by multiplying by $\frac{180}{\pi }$. So, $\theta =\arctan (0.12)\times \frac{180}{\pi }$