MathNet 2019-part-06 — 184 problems (EN–VI) Question 169

Consider a triangle $ABC$ and a point $D$ on the side $AC$. If $\overline{AB} = \overline{DC} = 1$, $\angle DBC = 30^{\circ}$ and $\angle ABD = 90^{\circ}$, compute the value of $\overline{AD}$.