+826 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
+129845 P
5 8
Q M R
11
Law of Cosines { cos PMQ = - cos PMR }
PQ^2 = QM^2 + PM^2 - 2(QM * PM) * (-cos PMR)
PR^2 = RM^2 + PM^2 - 2 (RM * PM) * ( cos PMR)
5^2 = 5.5^2 + PM^2 + 2(5.5 * PM)cos(PMR)
8^2 = 5.5^2 + PM^2 - 2(5,5 * PM) cos (PMR) add these
5^2 + 8^2 = 2 * 5.5^2 + 2PM^2
89 = 60.5 + 2PM^2
28.5 / 2 = PM^2
14.25 = PM^2
sqrt (14.25) = PM ≈ 3.77
