+936 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
+129847 P
5 8
Q M R
5.5 5.5
Law of Cosines (twice)
PR^2 = PQ^2 + QR^2 - 2(PQ * QR) cos (angle Q)
8^2 = 5^2 + 11^2 - 2(5 * 11) cos (angle Q)
[8^2 - 5^2 -11^2 ] / [ -110] = cos (angle Q) = 41/55
PM^2 = QM^2 + QP^2 - 2 ( QM * QP) cos (angle Q)
PM^2 = (5.5)^2 + 5^2 - 2 ( 5.5 * 5) (41/55)
PM^2 = 14.25
PM = sqrt (14.25) ≈ 3.78
