Probability — practice question

A non-uniform rod $AB$ has weight $6\text{ N}$ and is in limiting equilibrium, with end $A$ touching a rough vertical wall. The length $AB = 1.2\text{ m}$, the centre of mass of the rod is $0.8\text{ m}$ from $A$, and the angle between $AB$ and the downward vertical is $\theta^\circ$. At $B$, a force of magnitude $10\text{ N}$, acting at an angle of $30^\circ$ to the upwards vertical, is applied to the rod (see diagram). The rod and the line of action of the $10\text{ N}$ force both lie in a vertical plane perpendicular to the wall.