Trigonometry · Hard problem

Points $A$ and $C$ lie on a straight shoreline, $100$ m apart, and a buoy $B$ floats offshore. At $A$, the sight line to the buoy makes a $30^\circ$ angle with ray $AC$. At $C$, the sight line to the buoy makes a $45^\circ$ angle with the shoreline continued beyond $C$ (away from $A$). How far is the buoy from the shoreline, in metres? Give an exact answer.