Answer
$40.0lb$
Work Step by Step
The tension in the string is given as
$\Sigma F_x=-F+2Tcos\theta=0$
This can be rearranged as:
$T=\frac{F}{2cos\theta}$
We plug in the known values to obtain:
$T=\frac{287}{2cos69.0^{\circ}}$ The angle $\theta$ is $\theta=\frac{1}{2}(138^{\circ}=69.0^{\circ})$
$T=40.0lb$
