Question: solve for the weight that would allow for equilibrium relative to the counterweight. use moment equilibrium from the top of the mast to cancel tensions

solve for the weight that would allow for equilibrium relative to the counterweight. use moment equilibrium from the top of the mast to cancel tensions and the normal force from the mast.
After, you can also do force equilibrium to solve for the mast force and the tension in the cables, and verify the weight with these as well. The main intention is to solve for the weight W though.
solve for the weight that would allow for

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