+1678 Plz help Im stuck
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
+129771 P
5 8
Q M R
11
Law of Cosines
PR^2 = QR^2 + PQ^2 - 2(QR * PQ) cos (PQR)
8^2 = 11^2 + 5^2 - 2 ( 11 * 5) cos (PQR)
cos (PQR) = [ 8^2 - 11^2 - 5^2 ] / [ -2 * 11 * 5] = 41/55
QM = 11/2 = 5.5
Law of Cosines again
PM^2 = QM^2 + PQ^2 - 2 (QM * PO) cos (PQR)
PM^2 = 5.5^2 + 5^2 - 2 ( 5.5 * 5) ( 41/55)
PM = sqrt [ 5.5^2 + 5^2 - 2 ( 5.5 * 5) ( 41/55) ] ≈ 3.77
