
Arturo O. answered 01/20/18
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Using i and j for E and N respectively,
Wind velocity:
w = 30cos45ºi - 30sin45ºj = 21.21i - 21.21j
Airplane in still air:
u = 200sin60ºi + 200cos60ºj = 173.21i + 100j
Resultant:
v = w + u = (21.21 + 173.21)i + (-21.21 + 100)j = 194.42i + 78.79j
v = √(194.422 + 78.792) = 209.8 km/h
Direction (north of east):
tan-1(vy/vx) = tan-1(78.79/194.42) = 22.1°
I get the same answer as you.