Define angle of repose and find the relation between angle of repose and angle of friction.

Angle of repose is the angle that an inclined plane makes with the horizontal when a body placed on it just starts sliding down.
Let a body of weight W be placed on rough inclined plane and the body just starts sliding when angle of inclination is ϕ. W can be resolved into two components:
(i) W sinϕ along the plane.
(ii) W cosϕ perpendicular to the plane.

  When body is just at the point of sliding, then
                
or                                   ...(1)
       We know the relation between angle of friction is
                                         ...(2)
From (1) and (2),
                         
or