Answer
$100 \sqrt 7 N \approx 264.6 N$ ; $\approx 139.1 ^\circ$
Work Step by Step
$u= (300 cos 180) i+(300sin 180)j =\lt -300,0 \gt$
$v= (200 cos 60) i+(200 sin 60)j =\lt 200 (1/2), 200 ( \sqrt 3/2) \gt = \lt 100, 100 \sqrt 3 \gt$
Resultant force, F: $\lt -300,0 \gt+\lt 100, 100 \sqrt 3 \gt= \lt -200, 100 \sqrt 3 \gt $
$|F|=\sqrt {(-200) ^2+(100 \sqrt 3 )^2} N= 100 \sqrt 7 N\approx 264.6 N$
$\theta =180 ^\circ+arctan[\dfrac{vertical}{horizontal}]$
$\theta =180 ^\circ+arctan\frac {100 \sqrt 3} {-200}$
$ \theta \approx 139.1 ^\circ$
