Suspended steel beam

I'm having problems with what equation to use for this question:
A 1000 kg steel beam is supported by two ropes. Each rope has a maximum sustained tension of 6000N. Does either rope break?
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 Recognitions: Homework Help Science Advisor Draw a free body diagram. The two tensions are directed along the ropes. The sum of the tensions is directed upwards and has magnitude F=mg (m=mass of the beam).
 Well, the weight causes a force of roughly 10*1000 = 10000 [N] on both ropes combined. But because of different angles, the forces caused by the ropes will not be the same. Let F1 be the force of the left rope (20 degree angle), and F2 the other force. You know that the forces will have to keep the weight up, so the vertical components together must add up to 10000 [N] : F1 sin[20] + F2 sin[30] = 10000 Now the horizontal components will be directed in opposite direction, and will, because of that, have to be of equal size. So: F1 cos[20] - F2 cos[30] = 0 You can solve F1 and F2 from these equations, and check if any of the ropes will break.