+506 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
+129630 cos RMP = -cos QMP
Law of Cosines
PQ^2 = QM^2 + PM^2 - 2(QM * PM)cos (QMP)
PR^2 = RM^2 + PM^2 - 2(RM * PM) (-cos QMP)
18^2 = 12.5^2 + PM^2 - 2(12.5*PM)cos (QMP)
23^2 = 12.5^2 + PM^2 +2(12.5 * PM)cos(QMP) add these
853 = 312.5 + 2PM^2
[853 -312.5] / 2 = PM^2
540.5 / 2 = PM^2
PM = sqrt [ 540.5/2 ] ≈ 16.44
