Olympiad Geometry · Medium problem

Triangle $ABC$ has $AB = 8$, $AC = 12$, and $m\angle A = 55^\circ$. Points $D$ on $\overline{AB}$ and $E$ on $\overline{AC}$ satisfy $AD = 6$ and $AE = 9$. Determine whether $\triangle ADE \sim \triangle ABC$ by SAS$\sim$, then find $DE$ given $BC = 15$.