# Math Help - angle between two ropes

1. ## angle between two ropes

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?

2. ## tug of war

Originally Posted by 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?
Hi chengbin,

I set up two force diagrams for Allie and Beth.Cathy pulled with a force of70N so the opposing force has to be 70N.Theforces perpendicular to 70 must be equal and opposite By setting up two equations in xand y the lateral force is 18.5 .The 30N diagram gives opposing force 23.6 and the 50N diagram opposing force is 46.4 I got 59.8 for the angle between Allie and Beth's ropes using tangents to determine the acute angles in each force diagram

bjh