Velocity of the plane relative to the air:
[tex]\vec v_{P/A}=240(\cos110^\circ,\sin110^\circ)\,\mathrm{mph}[/tex]
Velocity of the air relative to the Earth:
[tex]\vec v_{A/E}=56(\cos325^\circ,\sin325^\circ)\,\mathrm{mph}[/tex]
Velocity of the plane relative to the Earth:
[tex]\vec v_{P/E}=\vec v_{P/A}+\vec v_{A/E}[/tex]
[tex]\vec v_{P/E}=(240\cos110^\circ+56\cos325^\circ,240\sin110^\circ+56\sin325^\circ)\,\mathrm{mph}[/tex]
[tex]\vec v_{P/E}\approx(-36.21,193.41)\,\mathrm{mph}[/tex]
The plane's speed is
[tex]\|\vec v_{P/E}\|\approx\sqrt{(-36.21)^2+193.41^2}\approx196.77\,\mathrm{mph}[/tex]
and its direction [tex]\theta[/tex] is given by
[tex]\tan\theta\approx\dfrac{193.41}{-36.21}\implies\theta\approx100.6^\circ[/tex]
I think there may be a typo in one of the answer choices. The closest answer would probably be C. Someone must have dropped the ball when coming up with the question...
