How Do You Solve the Moving Pulley Problem with a 100 kg Sack for Equilibrium?

[Jay9313]

Homework Statement

http://media.cheggcdn.com/media/76d/76dd5c56-43a5-44d3-b8b8-40ba63a9010a/phpYYNJyN.png

Cable ABC has a length of 5 m. Determine the position x and the tension developed in ABC required for equilibrium of the 100 kg sack. Neglect the size of the pulley

Homework Equations

T_ABCosθ + T_BCCos$\phi$=0
T_ABSinθ + T_BCSin$\phi$=980N
I also have the distance from C to the pulley (in x direction) is 3.5-x

The Attempt at a Solution

My attempt at the solution so far is
T_ABCosθ = T_BCCos$\phi$
I can rearrange the trig functions themselves, but I'm missing a height component, but I don't even know if that's the right track.

 

[Jay9313]

I have also managed to introduce a few new variables. I have introduced h+H=5 (The length of the rope) and y and y+0.75

 

[haruspex]

Consider the 'free body' diagram for a thin vertical slice of the rope directly under the pulley (thin compared with radius of pulley). What does this tell you about the tension each side?

 

[bigu01]

Tension is the same. I tried to find similar triangles and worked with them but I am getting equations with x^4.