Answer
The ship should sail 354 km at an angle of $45.3^{\circ}$ south of east.
Work Step by Step
We can find the east component $d_x$ of the direction $d$.
$d_x - 285~cos(62.0^{\circ}) = 115~km$
$d_x = 115~km + 285~cos(62.0^{\circ})$
$d_x = 248.8~km$
We can find the south component $d_y$ of the direction $d$.
$d_y - 285~sin(62.0^{\circ}) = 0$
$d_y = 285~sin(62.0^{\circ})$
$d_y = 251.6~km$
We can use $d_x$ and $d_y$ to find the magnitude of the distance $d$.
$d = \sqrt{(248.8~km)^2+(251.6~km)^2}$
$d = 354~km$
We can find the angle south of east.
$tan(\theta) = \frac{251.6}{248.8}$
$\theta = tan^{-1}(\frac{251.6}{248.8}) = 45.3^{\circ}$
The ship should sail 354 km at an angle of $45.3^{\circ}$ south of east.