Vector Components: Equal Force of Two Wires Suspending 500N Sign

[Coco12]

Homework Statement

two wires are used to suspend a sign that weighs 500N. the two wires make an angle of 100 degrees between each other. If each wire is exerting an equal amount of force, how much force does each wire exert?

Homework Equations

The Attempt at a Solution

The answer is 389.. but I don't understand how to get that.. Can someone please explain. Thanks

 

[cepheid]

Draw a free body diagram for the sign. What are ALL the forces that act on it? Since the sign is not moving, what must be true about the vector sum of these forces? Now pay attention to the vertical components of those forces...how would you use trigonometry to figure out what these are?

 

[Bryson]

Also note, that both wires are exerting equal force. Exploit symmetry.