What percentage grade should a road have if the angle of elevation of the road is 6 degrees? (The percentage grade is defined as the change in the altitude of the road over a 100-foot horizontal distance. For example a 5% grade means that the road rises 5 feet for every 100 feet of horizontal distance.)

Question

Mathematics

Isai Le

8 August, 15:16

What percentage grade should a road have if the angle of elevation of the road is 6 degrees? (The percentage grade is defined as the change in the altitude of the road over a 100-foot horizontal distance. For example a 5% grade means that the road rises 5 feet for every 100 feet of horizontal distance.)

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Answers (1)

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Morgan Pacheco · Answer 1

10.5%

Step-by-step explanation:

The tangent of the angle is the ratio of rise to run.

tan (angle) = grade

tan (6°) ≈ 0.105 = 10.5%

The grade will be 10.5% for an angle of elevation of 6°.