Compute the components of the given vectors. Let [tex]P[/tex] denote the plane's velocity vector, and [tex]W[/tex] the wind. Then
[tex]P=\langle P_x,P_y\rangle=\langle250\cos(-40^\circ),250\sin(-40^\circ)\rangle[/tex]
[tex]\implies P=\langle191.5,-160.7\rangle[/tex]
[tex]W=\langle35\cos(-120^\circ),35\sin(-120^\circ)\rangle=\langle-17.5,-30.3\rangle[/tex]
The resultant velocity (rounded) is
[tex]P+W=\langle174,-191\rangle[/tex]
with magnitude [tex]\sqrt{174^2+(-191)^2}=258[/tex] and direction [tex]\tan^{-1}\frac{-191}{174}=-47.7^\circ[/tex], or about 258 mi/hr at 47.7 degrees south of east.
