Define Angle of Friction and show coefficient of static friction is Equal to tangent of the angle of friction

Angle of Friction : The angle between the normal reaction and the resultant of limiting force of friction and normal reaction is called angle of friction.

The resultant of limiting friction (F) and normal reaction (R') is represented by R = OC. the angle $\theta$ between R and R' is called angle of Friction.

Now $tan \theta = \frac{(f_{s})_{max}}{R} = \frac{F}{R}$

But $\frac{F}{R} = \mu_{s}$(co-efficient of static friction)

$\therefore tan\theta = \mu_{s}$

Thus , co-efficient of static friction is numerically equal to the tangent of the angle of friction.