Task B-4.5. On the chord $\overline{A B}$ of the circle $k(S, r)$, two isosceles triangles are constructed on the same side of the chord, with the chord $\overline{A B}$ being their common base. One has its third vertex at the center $S$, and the other at a point $C$ on the circle. If the ratio of their areas is $3:(2 \sqrt{3}+3)$, calculate the measure of the angle between the legs of the triangle $\triangle A B S$.