The velocity of the air relative to the ground is
[tex]\vec v_{A/G}=\left(95\,\frac{\rm km}{\rm h}\right)(\cos30.0^\circ\,\vec\imath+\sin30.0^\circ\,\vec\jmath)[/tex]
The velocity of the plane relative to the air is
[tex]\vec v_{P/A}=\left(301\,\frac{\rm km}{\rm h}\right)(\cos\theta\,\vec\imath+\sin\theta\,\vec\jmath)[/tex]
where [tex]\theta[/tex] is the direction the plane needs to point so that the resultant vector - the velocity of the plane relative to the ground - is
[tex]\vec v_{P/G}=\vec v_{P/A}+\vec v_{A/G}=v(\cos13.0^\circ\,\vec\imath+\sin13.0^\circ\,\vec\jmath)[/tex]
Here [tex]v[/tex] is the speed of the plane relative to the ground.
So we have
[tex]\begin{cases}v\cos13.0^\circ=\left(95\,\frac{\rm km}{\rm h}\right)\cos30.0^\circ+\left(301\,\frac{\rm km}{\rm h}\right)\cos\theta\\v\sin13.0^\circ=\left(95\,\frac{\rm km}{\rm h}\right)\sin30.0^\circ+\left(301\,\frac{\rm km}{\rm h}\right)\sin\theta\end{cases}[/tex]
Use a calculator to solve for [tex]v[/tex] and [tex]\theta[/tex]; you should find
[tex]v=390\,\frac{\rm km}{\rm h}[/tex]
[tex]\theta=7.7^\circ[/tex]
