Answer
$F_B = 241~N$
Work Step by Step
The horizontal components of $F_A$ and $F_C$ must be equal and opposite. We can find the angle $\theta$ of the direction of $F_C$ above the horizontal:
$F_A~cos ~47^{\circ} = F_C~cos~\theta$
$\theta = cos^{-1}~(\frac{F_A~cos 47^{\circ}}{F_C})$
$\theta = cos^{-1}~[\frac{(220~N)~cos 47^{\circ}}{170~N}]$
$\theta = 28^{\circ}$
The sum of the vertical components of $F_A$ and $F_C$ must be equal and opposite to $F_B$. We can find $F_B$:
$F_B = F_A~sin~47^{\circ}+F_C~sin~28^{\circ}$
$F_B = (220~N)~sin~47^{\circ}+(170~N)~sin~28^{\circ}$
$F_B = 241~N$
