2016 Pascal Problem 23

In the diagram, \triangle PQR is isosceles with PQ = PR = 39 and \triangle SQR is equilateral with side length 30. The area of \triangle PQS is closest to

\textbf{(A)}\ 68\quad \textbf{(B)}\ 75\quad \textbf{(C)}\ 50\quad \textbf{(D)}\ 180\quad \textbf{(E)}\ 135

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.