The angle between the resultant contact force and the normal force exerted by the body on the other is called the angle of friction. Show that if  be the angle of friction and  the coefficient of static friction,   tan^-1 .

 

 

Here,

tan  = f/N (completing the parallelogram)

 

we know that ,

f   N (static friction is self adjusting)

 

=> tan  = f/N

=> tan    N / N

 

Therefore,  

 

   tan^-1 .

 

Hope this helps .. cheers !!