A331 n stoplight is hanging in equilibrium from cables as shown. the tension in the right cable is 550 n, and it makes an angle of 12 degrees with the horizontal.

what is the force of tension exerted by the cable on the left side?

The correct answer is 580.

The upward force the right tension cord exerts on the traffic light is equal to about 114.35 N. Because the stoplight is being help upright the natural force (upward force) provided by both tension cords must be equal to the gravitational (downward) force of the traffic light which is 331.
If 114 is the upward force on the right side then 216 N must be the force provided by the left side.
You then have a right triangle with the length opposite theta = about 216 and theta = 22. So sin(22)* X = 216, where X is the length of the hypotenuse, or the force found in the left cord.
with sig figs added to the mix the answer is 580 N

I believe the answer is true to the E dgenuity physics course 

Go to the bathroom and vape