Question 37
Right triangle $\triangle DEF$ with $\angle D = 90^{\circ}$ and $\angle F = 30^{\circ}$ is inscribed in equilateral triangle $\triangle ABC$ such that $D$, $E$, and $F$ lie on segments $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively. Given that $BD = 7$ and $DC = 4$, compute $DE$.