Calculating Cable Angles for Suspended Beam

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To find the resting angles of the cables supporting a beam with two weights, the tensions T1 and T2 in the cables must be analyzed. The x-components of the tension must cancel out, leading to the equation T1x = T2x. The y-components must balance the weights, resulting in T1y + T3y + W1 = 0 and T2y + T3y + W2 = 0. Given the weights W1 and W2, along with the angle B, the calculations can be simplified to determine the angles θ1 and θ2. The problem emphasizes achieving a stable, resting position for the system.
3wt Man
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I have a beam suspended by two cables with two weights suspended by the beam. The weight of the beam is negligible. How would I find the resting angles of the cables.
 

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Take T1 to be the tension in one cable, T2 the tension in the other. Take \theta1 to be the angle the first cable makes with the horizontal, \theta2 to be the angle the second cable makes. You can calculate the x and y components of both tension vectors in terms of T and \theta. You know what the y component of each must be- they are given. You know that the x components must cancel, because the beam does not move left or right.
 
This is not a homework problem!
It has been so long since I did anything like that.
I have
T1x=T2x
T1y+T3y+W1=0
T2y+T3y+w2=0

Then I get lost
 
Okay I worked it out again, I finally get to a point where a Angle C = something Angle A.
This needs to be in a resting position and that is where my problem is.
W1=350lbs W2=650lbs B=20Deg
 

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