Hello GalaxieFiable2952!
In this problem, you can assume that the sign will be safely hanged when the system will be at equilibrium. In this case, you have to make sure that the forces cancel each other out.
With the given information, it is possible to get the value for the weight of the sign and for the tension in the beam.
Since we want the system to be at equilibrium, we want to install a cable who will act as an equilibrant force on the sign, so that the resultant force will be zero on both x and y axes.
With this information, we can develop formulas for the resultant force on both axes. You can then isolate the value of the angle to find it!
I hope this will help you! Don't hesitate to reach out if you have another question!
Éveline