Probability — practice question

A uniform lamina weighing $15\text{ N}$ is shaped as a trapezium $ABCD$, with the measurements shown in the diagram. The lamina is hinged freely 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).