Define angle of friction

Explanation

The angle of friction is defined as the angle between the normal force (N) and the resultant force (R) of normal force and maximum friction force `(f^(mas))`

In figure the resultant force is `R = sqrt( (f_(s)^(max))^2 + N^2)`
`tan theta = (f_(s)^(max) )/(N)` ......(1)
But from the frictional relation, the object begins to slide when `f_(s)^(max) = mu_s N`
or when `(f_(s)^(max) )/(N) = mu_s`
From equations (1) and (2) the coefficient of static friction is
`mu_s = tan theta`
The coefficient of static friction is equal to tangent of the angle of friction