Question

A ladder is leaning against a vertical wall. There is negligible friction between the ladder and the wall, and the coefficient of static friction between the ladder and the ground is 𝜇s=0.245. The ladder is uniform, with its center of gravity located at its geometric center.
The figure shows a cut away side view of the ladder described in the problem. The ladder rests diagonally with the top of the ladder against a vertical wall at the left of the figure and the bottom of the ladder against the floor at the bottom of the figure. The acute angle between the vertical wall and the angled ladder is labeled alpha. Separately, an X Y coordinate system is drawn in the upper right corner of the figure. The Y axis points up and the X axis points to the right.
At what maximum angle 𝛼, relative to the wall, can the ladder lean without slipping?