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Three men are trying to hold a ferocious lion still for the veterinarian. The lion, in the center,is wearing a collar with three ropes attached to it and each man has hold of a rope. Charlie is pulling in the direction N60 W with a force of 350 pounds and Sam is pulling in the direction N45E with a force of 400 pounds. What is the direction and magnitude of the force needed on the third rope to counterbalance Sam and Charlie.(Draw a diagram 1st)

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Nirina7
the answer 
the third rope to counterbalance Sam and Charlie is F
and vectF +vectF1 +vectF2 =vect0
let's consider axis
y'y  vectF = -F
      vectF 1= F1cos60
      vectF 2= F2cos45
-F = -F1cos60-F2co45
so F= F1cos60+F2co45= 350x0.5+400x0.7=457.84 pounds

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