#### Answer

$F=917lb$
$\theta=31.8^{\circ}$

#### Work Step by Step

We are asked to determine the magnitude of $F$ and its direction, $\theta$
Given that the force on member AB is 650lb and the force of member BC is 500lb, we can apply the law of cosines to find the magnitude of $F$.
$c=\sqrt{a^2+b^2-2*a*b*\cos(C)}$
$c=\sqrt{500^2+650^2-2*500*650*\cos(105^{\circ})}$
$c=917$
$F=917lb$
Using this result, we can apply the law of sines to find the$ \theta$
$\sin\theta / 500 = \sin 105^{\circ} / 917$
Solving for $\theta$, we obtain:
$\theta=31.8^{\circ}$