Answer
5.31$^o$ west of south.
Work Step by Step
Call east the positive x direction and north the positive y direction.
Let P denote the Plane, A the Air, and G the Ground. The pair “PG”, for example, represents the plane’s motion relative to the ground.
$$ \vec{v_{PG}} = \vec{v_{PA}} + \vec{v_{AG}} $$
$$(0, V) = (688 cos \theta, 688 sin \theta) km/h + (90.0 cos 45 ^{\circ}, 90.0 sin 45 ^{\circ}) km/h$$
Equate the x-components on both sides to solve for the angle of 264.69$^o$, or approximately 5.31$^o$ west of south.
