+1557 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
+129895 P
5 8
Q M R
11
Law of Cosines
PR^2 = QP^2 + QR^2 - 2(QP * QR)cos(PQR)
8^2 = 5^2 + 11^2 - 2(5 * 11) cos (PQR)
64 = 25 + 121 - 110 cos (PQR)
[ 64 - 25 - 121 ] / [ -110] = 41/55 cos (PQR)
Law of Cosines again
PM^2 = QM^2 + PQ^2 - 2 (QM * PQ)cos (PQR)
PM^2 = (5.5)^2 + 5^2 - 2(6.5 * 5) (41/55)
PM^2 = 14.25
PM = sqrt [14.25 ] ≈ 3.77
