Answer
$T = \frac{W~x}{L~sin~\theta}$
Work Step by Step
We can consider the net torque about the rotation axis at the hinge.
The torque due to the box's weight must be equal in magnitude to the torque due to the tension in the wire.
We can find an expression for the tension:
$L~T~sin~\theta = mg~x$
$L~T~sin~\theta = W~x$
$T = \frac{W~x}{L~sin~\theta}$
