Need help determining force behind certain vectors

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Are you planning on using Newton's Laws? They can give you a start.
 
You can also use the sine rule since the system is in equilibrium. sina/a=sinb/b=sinc/c where a,b,c are the lengths of the sides and the sina/b/c represent the sine of the angle opposite the side a/b/c.
 
Make a FBD of the weight with the 2 cables cut. Sum forces in the horiz and vert directions to get the force in each cable.
 

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