Draw and label a diagram:
Mark the starting point as A. Draw a line due west (to the left) ending at point B.
The plane changes direction to 190°. This is measured from due North. This results in an angle at B of 100° from AB.
The plan is traveling South by West.
Draw a line from B at this angle ending at C. Connect AC.
Using the Law of Cosines:
AC2 = AB2 + BC2 - 2(AB)(BC)cos B.
AC2 = 14400 + 57600 - 57600 cos 100°
AC2 = 72000 - 57600(-0.173648178)
AC2 ≈ 72000 + 10002
AC2 ≈ 82002
AC ≈ 286.359913