Equilibrium in a tractive apparatus - tension and pulleys

[sethro_gt]

Homework Statement

Determine the magnitude and direction (theta) of F in the diagram of

Homework Equations

ΣFx = 0
ΣFy = 0
F = ma

The Attempt at a Solution

I tried using the sum of components but I end up with three variables and two equations. I've always had issues with figuring out tension through a pulley system. I'm hoping for some insight as to what parts of the diagram are relevant to finding F.

So far I've figured F(ab) = cos45(98N) = 138.6N but I can't figure out how to relate that to F and Fac and Fcd.

is Fcd equal to ΣFy?

This is from my statics book and my physics text isn't helping either.
Any clues are appreciated, thanks.

 

[sethro_gt]

Ok I think I got it. Someone else posted a similar problem that I didn't find before.

So tension is the same through the entire rope = 98N

Knowing that I found the x & y components of the two known angles, 45 and 75. These components have to combine with those of F to equal 0. Then I found they theta with these values.

I hope it is this simple...