Probability — practice question

A lamina of uniform density and weight $15\,\text{N}$ is shaped as trapezium $ABCD$, with the measurements shown in the diagram. It is freely hinged at $A$ to a fixed point. One end of a light inextensible string is fastened to the lamina at $B$. The lamina is in equilibrium with $AB$ horizontal; the string is taut, lies in the same vertical plane as the lamina, and is inclined at an angle of $30^\circ$ above the horizontal (see diagram).