Answer
$582.39 \ mph$
Work Step by Step
We are given that $ \theta_{w} = 225^{\circ}$ and $\theta_{v} = 118^{\circ}$
We know that $v=||v|| \lt \cos \theta , \sin \theta \gt $
Thus, $w=60 \lt \cos 225^{\circ} , \sin 225^{\circ} \gt$
and $v=580 \lt \cos 118^{\circ} , \sin 118^{\circ} \gt$
Now, $w= \lt 60 \cos 225^{\circ} , 60 \sin 225^{\circ} \gt$
and $v= \lt 580\cos 118^{\circ} ,580 \sin 118^{\circ} \gt$
Therefore, $w+v= \lt 60 \cos 225^{\circ} , 60 \sin 225^{\circ} \gt + \lt 580\cos 118^{\circ} ,580 \sin 118^{\circ} \gt=\lt -229.867, 535.111 \gt$
So, $\sqrt {(-229.867)^2+(535.111)^2}=582.39 \ mph$
