Answer
$40^{\circ}$.
Work Step by Step
From the textbook, “An object whose center of gravity above its base of support will be stable if a vertical line projected downward from the center of gravity falls within the base of support.”
The box just begins to tip when a vertical line down from the center of gravity is at the lowest corner. This is an unstable equilibrium, and the box falls over if the surface is inclined any more. At that point, the tangent of the angle is half the side length, 1.0 m, divided by the height of the CG, 1.18 m.
$$tan \; \theta=\frac{1.0\;m}{1.18\;m}$$
$$\theta = tan^{-1}\frac{1.0\;m}{1.18\;m}=40^{\circ}$$
