Representation of data — 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. $AB = 1.2\,\text{m}$, 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 $10\,\text{N}$ is applied at an angle of $30^\circ$ to the upwards vertical (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.