+1439 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
+129885 
cos PMR = -cos PMQ
Law of Cosines (twice)
PO^2 = QM^2 + PM^2 - 2(QM * PM) cos PMQ
PR^2 = RM^2 + PM^2 - 2(RM * PM) ) (-cos PMQ)
18^2 = 12.5^2 + PM^2 - 2(12.5 * PM) cos PMQ
23^2 = 12.5^2 + PM^2 + 2(12.5 * PM) cos PMQ add these
18^2 + 23^2 = 2*12.5^2 + 2PM^2
853 = 312.5 + 2PM^2
540.5 = 2PM^2
270.25 = PM^2
sqrt [270.25] = PM ≈ 16.44
