We are asked to determine the angle of repose given the coefficient of static friction. To do that we will use the following relationship:
[tex]\tan \theta=\mu_s[/tex]
Where:
[tex]\begin{gathered} \theta=\text{ angle of repose} \\ \mu_s=\text{ coefficient of static friction} \end{gathered}[/tex]
We solve for the angle of repose by taking the inverse tangent function:
[tex]\theta=\tan ^{-1}(\mu_s)[/tex]
Now we substitute the first value:
[tex]\theta=\tan ^{-1}(0.25)=14.04[/tex]
For the second value we get:
[tex]\theta=\tan ^{-1}(0.5)=26.57[/tex]
Therefore for the first surface pairs, we have angles of repose: 14.04 - 26.57
