To determine the percentage grade that should be put on a road sign where the angle of elevation of the road is 9 degrees, what function would be most helpful?

Question

Many mountainous areas have had road signs like this sign that refer to the percentage grade for the road. An 8% grade, for example means that the altitude changes by 8 feet for each 100 feet of horizontal distance.

Answer 1

θ = the elevation angle

 

Have you had trigonometry?  If so, note that the ratio of the percent of grade to 100 is the tangent of the elevation angle. So for 9° elevation,

 

tan9° = x/100

 

x = 100 tan9° ≅ 15.84%

 

The general formula for an elevation angle θ is

 

% grade = 100 tanθ = 100 x (the tangent function of the elevation angle)