Answer
The maximum angle of a rock that can be walked on without slipping is $50^{\circ}$.
Work Step by Step
If the climber is walking without slipping, then the force of static friction directed up the slope is equal to the component of the weight directed down the slope. To find the maximum possible angle, we can assume that the force of static friction is at its maximum possible value.
$mg~sin(\theta) = mg~cos(\theta)~\mu_s$
$tan(\theta) = \mu_s$
$\theta = arctan(1.2)$
$\theta = 50^{\circ}$
The maximum angle of a rock that can be walked on without slipping is $50^{\circ}$.
