What Is the Maximum Tension a Block Can Suspend at Equilibrium?

[unknown_2]

Homework Statement

Determine the maximum weight W of the block that can be suspended in the position shown if each cord can support a max tension of 80lb. also what is the angle \theta for equilibrium?

Homework Equations

The Attempt at a Solution

the free body diagram should be:
-force A to B is 60^{o} from the positive x axis
-force from the block is in the negative y direction
-tension is in the third quadrant at and angle of \theta from the negative y axis

putting the forces in their respected x and y components:
**note: I'm using 30^{o} instead of the 60 from the x axis**

F_{x} = 80sin30 - Wsin\theta = 0
F_{y} = 80cos30 - Wcos\theta - W = 0

from F_{x} : W = \frac{80sin30}{sin\theta}

sub into F_{y}:

0=80cos30 - \frac{80sin30}{sin\theta}cos\theta - \frac{80sin30}{sin\theta}

then i get:
cot30 = \frac{cos\theta - 1}{sin\theta}
form here I'm not sure how to solve for \theta. the angle should b 60 deg, but from the solution, it seems to me lyk a random guess...

any help would b appreciated.
cheers

 

[unknown_2]

any1?

 

[LowlyPion]

Is θ constrained to be less than 90°?

Because at greater than 90° more weight can be supported it seems, because the Tension of the rope no longer has a negative y component.