 18
 4
 Homework Statement
 For the apparatus shown in the figure, find the equilibrium angle θ in terms of the two masses.
 Homework Equations

(1) ΔE = ΔU + ΔK = 0 (Conservation of energy)
(2) ΔE = 2My₁ + mgy₂ = 0
The solution is an application of the law of conservation of energy.
Start with equation (1). The masses are in equilibrium and are not accelerating. This implies that ΔK = 0, because the kinetic energy will not change without acceleration. Thus, we are left to find equation (2) in terms of θ.
Finally, we set up a geometry problem to find substitutions for the heights in equation (2).
This is where I fail. I can't find the heights in terms of the angle without introducing extra variables. I have tried constructing multiple triangles and applying some basic geometry and trigonometry, but to no success (pythagorean, law of sines, etc...).
Any hints or ideas would be greatly appreciated.