+1520 In triangle PQR, M is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
+130070 P
5 8
Q M R
5.5 5.5
Note that 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)
5^2 = 5.5^2 + PM^2 - 2(5.5 * PM) cos (QMP)
8^2 = 5.5^2 + PM^2 + 2(5.5 *PM) cos (QMP) add these
89 = 60.5 + 2PM^2
28.5 = 2PM^2
PM = sqrt [ 28.5 / 2 ] ≈ 3.77
