Question 141
Let $ABCD$ be an isosceles trapezoid with $AB = 1$, $BC = DA = 5$, $CD = 7$. Let $P$ be the intersection of diagonals $AC$ and $BD$, and let $Q$ be the foot of the altitude from $D$ to $BC$. Let $PQ$ intersect $AB$ at $R$. Compute $\sin \angle RPD$.