Answer
The crew should fly 351 km at an angle $11.8^{\circ}$ south of east.
Work Step by Step
We can find the east component of the distance $d_x$.
$d_x = 170~sin(68.0^{\circ}) + 230~cos(36.0^{\circ})$
$d_x = 343.7~km$
We can find the north-south component of the distance $d_y$.
$d_y = 170~cos(68.0^{\circ}) - 230~sin(36.0^{\circ})$
$d_y = -71.5~km$
Note that the negative sign means that the plane ended up 71.5 km to the south.
We can use $d_x$ and $d_y$ to find the distance.
$d = \sqrt{(343.7~km)^2+(-71.5~km)^2}$
$d = 351~km$
We can find the angle $\theta$ south of east.
$tan(\theta) = \frac{71.5}{343.7}$
$\theta = tan^{-1}(\frac{71.5}{343.7}) = 11.8^{\circ}$
The crew should fly 351 km at an angle $11.8^{\circ}$ south of east.
