+250 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
+128578 Law of Cosines
18^2 = 12.5^2 + PM^2 - 2 ( 12.5 * PM) cos (QMP)
23^2 = 12.5^2 + PM^2 - 2(12.5 * PM) (-cos (QMP)
Simplify
(18^2 - 12.5^2 - PM^2 ) / [ -25 PM ] = cos (QMP)
[23^2 - 12.5^2 - PM^2 ] / [ 25 PM = cos (OMP)
Equate cosines and simplify
- [ 167.75 - PM^2 ] = [372.75 - PM^2]
2PM^2 = 540.5
PM^2 = 270.25
PM =sqrt [ 270.25] ≈ 16.44
