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

[chengbin]

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?

 

[Stonebridge]

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.