PQR is a triangular park with PQ = PR = 200 m. A. T. V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively $45^{\circ},\; 30^{\circ}$ and $30^{\circ}$, then the height of the tower (in m) is :

Question

( A ) $50 \sqrt{2}$
( B ) $50$
( C ) $100 \sqrt{3}$
( D ) $100$