+1768 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
+129850 Law of Cosines
PR^2 = PQ^2 +QR^2 -2(PQ * QR)cos ( PQR)
23^2 =18^2 + 25^2 - 2(18 * 25) cos (PQR)
[23^2 - 18^2 - 25^2 ] / [ -2 * 18 * 25 ] = cos (PQR)
7/15 = cos (PQR)
Law of Cosines again
PM^2 = PQ^2 + (QR/2)^2 - 2(PQ * QR/2) cos (PQR)
PM^2 = 18^2 +(12.5)^2 - 2 (18 * 12.5)(7/15)
PM^2 = 270.25
PM = sqrt (270.25) ≈ 16.44
