An airplane flies between two points on the ground that are $500$ km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of $120$ m$/$s$.$ If a constant wind blows at $10\mathrm{.}0$ m$/$s due west $($relative to the ground$)$ during the flight, what direction must the plane fly $($relative to the north$)$ to arrive at the destination?$$

a$.$

$4\mathrm{.}78$west of north

b$.$

$85\mathrm{.}2$ west of north

c$.$

$4\mathrm{.}78$ east of north

d$.$

$4\mathrm{.}66$ west of north

e$.$

$4\mathrm{.}66$ east of north