In what direction, measured with respect to due west, should the pilot head the plane relative to the air?
"relative to the air" means when there is no wind blowing?
Anyway, if I understand what the Problem means,
the figure is that of a right triangle, with these:
---vertical leg = velocity of wind = 38 m/sec
---horizonta leg = unknown
---hypotenuse = velocity of plane when no wind blowing = 275 m/sec
---angle between horizopntal leg and hypotenuse = alpha = direction of plane to due West.
275sin(alpha) = 38
sin(alpha) = 38/275
alpha = arcsin(38/275)
alpha = 7.94265 degrees
Therefore, the plane should fly S 82.05735degrees W. --------------answer.