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 :\(\boxed{\text{The road should have a 10.51\% grade.}}\)