Determine the length of l (equilibrium)

[ND3G]

A ring of negligible size is subjected to vertical force P. Determine the required length l of the cord AC such that tension acting in AC is TAC. Also, what is the force acting in cord AB?

P = 300N, d = 0.2m (distance between A & B), angle ABC = 45 degrees, TAC = 250N

The graph basically looks like a "Y" with C & B at the tops, A at the centre and P the downward force.

Fx = 0; Fab(cos45) - 250cosx = 0
Fy = 0; Fab(sin45) + 250sinx - 300 = 0

Fab = (250cosx/cos45)

(250cosx/cos45)sin45 + 250sinx - 300 = 0

This is about as far as I get before I start mucking it up. Can some one help me through the steps to solve for "x" so I can eventually find l?

 

[weatherhead]

okay, if you're sure that's the equation you want to solve, then you should realize it's a pretty nasty beast. You're unlikely to get an exact answer, but you can tidy it up so it looks a lot nicer.
First, try dividing through by 50.
then, think what sin 45/cos 45 is (hint - trig identities)
in the end you've still got an equation that looks like this:
a cosx +b sin x +c = 0
this is an absolute pig to solve, your only chance is to do it numerically, or "translate" one of the functions into the other - do you know how to do this?? i.e cos(a)=sin(a+x)