let C weight be W
tension in C string=W
tension in B string=275
for equilibrium at A
balancing horizontal forces
Wcos30=275cosθ
balacing vertical forces
Wsin30+275sinθ=300
275cosθtan30+275sinθ=300
solving for θ we get
cosθ=0.188
θ=79.13 degrees
W=275*0.188/cos30
=59.7 lb
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