Answer
$86.03^{\circ};1.97KN$
Work Step by Step
We find the force components:
$F_x=8cos 30^{\circ}=6.93KN$
and $F_y=8 sin 30^{\circ}=4KN$
Thus $F_x=6+Fsin\theta-4sin 15^{\circ}=6.93$
$\implies Fsin\theta=1.9653$
and $F_y=Fcos\theta+4cos 15^{\circ}=4$
$\implies Fcos\theta=0.1363$
Now $tan\theta=\frac{1.9653}{0.1363}$
$\implies \theta=86.03^{\circ}$
and $F=\frac{1.9653}{sin\theta}$
$\implies F=1.97KN$
