Static Triple Vector Load Calculator

[splents]

Hi All,

I've been trying to figure out how to get this formula working for a few days now, and I *refuse* to give up.

There are three high points, with a line running down from each to a load W.
Each of the lines A,B,C are at different angles to each other (x-y plane), and each of the lines depart the load to the high points at different angles (z-plane).
The load is static, and there is no stretch or movement in the system.

By knowing only the angles of the lines and the weight of the load, how can I calculate the load on each line?

I have calculated this for a two rope system and it is simple trig, but for a three rope system I cannot seem to get it happening!
I've tried solving using trigonometry, but I keep getting stuck. Today I've been trying to solve simultaneous vectors, but I still can't seem to get it right.

If anyone has any clues, or could help I would greatly appreciate it.
I can also draw up a picture to show the system, if that helps.

 

[splents]

Some extra information that I've been trying to use for simultaneously solving is this;

If Vectors:
A=[Ai, Aj, Ak]
B=[Bi, Bj, Bk]
C=[Ci, Cj, Ck]

Then for the system to be static:
Ai + Bi + Ci = 0
Aj + Bj + Cj = 0
Ak + Bk + Ck = W