What is the angle between the ropes in a 3-way tug of war?

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In a 3-way tug of war involving Allie, Beth, and Cathy, the forces exerted are 30N, 50N, and 70N respectively. The system is in equilibrium, prompting a calculation of the angle between Allie's and Beth's ropes using the cosine law. The initial calculation yields an angle of 120 degrees, but the correct angle between the two ropes is actually 60 degrees. This discrepancy arises because the calculated angle represents the angle opposite to the force exerted by Cathy, not the angle between Allie's and Beth's ropes. Understanding the orientation of the forces is crucial for accurate angle determination.
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Allie, Beth, and Cathy are having a 3 way tug of war. Allie is pulling with a force of 30N, Beth with 50N, and Cathy with 70N. If the system is in equilibrium, what is the angle between Allie's rope and Beth's rope.

I used the cosine law, and

cos\theta=\frac{{30}^2+{50}^2-{70}^2}{2\cdot 30\cdot 50}
\theta = 120

But the answer is 60, because 180-120=60. Why?
 
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The angle you have calculated in the force triangle (shown by the arrow) is not the angle θ between the two ropes A and B.
forces.png
 
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