In order for the object not to slip, the component of the weight parallel to the surface must be equal to the frictional force (which acts in the opposite direction):
The parallel component of the weight is:
where m is the object mass and
is the angle of the inclined plane.
The frictional force is
where
is the coefficient of static friction.
Equalizing the two forces, we have
from which we find
and so, in our problem the coefficient of static friction must be
The parallel component of the weight is:
where m is the object mass and
The frictional force is
where
Equalizing the two forces, we have
from which we find
and so, in our problem the coefficient of static friction must be