Answer
$\phi=38.3^{\circ}$
Work Step by Step
Given that $\theta=30^{\circ}$ and the component of the 400lb force which acts up and to the left in the direction of AB is 600lb
$c=\sqrt{a^2+b^2-2*a*b*\cos(C)}$
$c=\sqrt{400^2+600^2-2*400*600*\cos(30^{\circ})}$
$c=322.97$
$F_{AC}=322.97lb$
Using this result, we can apply the law of sines to find $ \phi $
$\sin30^{\circ} / 322.97 = \sin \phi / 400$
Solving for $\phi$, we obtain:
$\phi=38.3^{\circ}$
