Answer
$F_{AB}=314lb$
$F_{AC}=256lb$
Work Step by Step
We can use the law of sines to find the magnitudes of the components of $F$.
$\sin75^{\circ}/350lb=\sin60^{\circ}/F_{AB}$
$F_{AB}=\sin60^{\circ} *350lb/\sin75^{\circ}$
$F_{AB}=314lb$
$\sin75^{\circ}/350lb=\sin45^{\circ}/F_{AC}$
$F_{AC}=\sin45^{\circ} *350lb/\sin75^{\circ}$
$F_{AC}=256lb$
