1103077008

Given a triangle $ABC$, the length of the median from $C$ is $9\mathrm{cm}$ and the length of the median from $B$ is $6\mathrm{cm}$. Let $T$ be the centroid, and $S$ be the midpoint of $AC$. The measure of the angle $BTC$ is ${120}^{\circ }$. Find the length of the side $AC$.