Answer:
Explanation:
A 9.0% grade corresponds to a road that rises 9.0 ft for every 100 ft along the horizontal.
• Let the angle of inclination that corresponds to a 9.0% grade = x
The diagram below is a representation of the problem:
Using trigonometrical ratios, we find the value of angle x.
[tex]\begin{gathered} \tan\theta=\frac{Opposite}{Adjacent} \\ \implies\tan x=\frac{9}{100} \end{gathered}[/tex]Take the arctan of both sides:
[tex]\begin{gathered} x=arctan(0.09) \\ x=5.1\degree \end{gathered}[/tex]The angle of the inclination that corresponds to a 9.0% grade is 5.1 degrees.
