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.)
Round your answer to two decimal places.
The road should have $a(n)$
Number $\%$ grade.
Answer
\(\boxed{\text{The road should have a 10.51\% grade.}}\)
Step 1 ：Given the angle of elevation is 6 degrees and the horizontal distance is 100 feet.
Step 2 ：Use the tangent function: \(\tan(6^\circ) = \frac{\text{change in altitude}}{100}\)
Step 3 ：Solve for the change in altitude: \(\text{change in altitude} = 100 \times \tan(6^\circ)\)
Step 4 ：Calculate the change in altitude: \(\text{change in altitude} \approx 10.51\)
Step 5 ：Convert the change in altitude to a percentage grade: \(\text{percentage grade} = 10.51\%\)
Step 6 ：\(\boxed{\text{The road should have a 10.51\% grade.}}\)
