Quote by twofish
I thought that I had to assume the tension in the cables, otherwise how would I solve for the parameters given, ie: "range of values of Q which the tension will not exceed 270 in either cable."
Do you not solve by setting each tension to max (270 N) and then solving for Q... let's say I get Magnitude Q = xN then I would say 0<= Q <= xN?
So far I have done this
sum Fx: 340 cos 0 + 270 cos 90 + 270 cos 180 + Qx cos 240
I then solved for Qx cos 240 = 70
sum Fy: 340 sin 0 + 270 sin 90 + 270 sin 180 + Qy sin 240
I then solved for Qy sin 240 = 270

I don't understand Qxcos240... Do you mean Qcos240? ie: Qx = Qcos240?
I don't think this method is correct... It is impossible for both tensions to be 270N at the same time.
I recommend going with what I said earlier... use T1 and T2 as variables.... solve for them in terms of Q... then you can see what limits are required to make T1 and T2 remain less than 270.