static equilibrium problem

[ShawnD1]

I have this crazy question I need to solve and don't know how to do it at all. The question reads:
Determine all the cable tensions and the mass of block E of the system shown in Figure P4-42. Use the vetor triangle method.

Here is the picture




The answers in the back are:
AB = 922N
BC = 631N
CD = 1190N
E = 126kg

The force due to gravity is m x 9.8 where m is mass in kg.

So far I have tried free body diagrams and a few trig ratios I pulled out of nowhere and I haven't gotten anywhere. I think I need to find the mass of E before I can start figuring out tensions.
Any suggestion on how I could try to get the answers would be appreciated .

[ILC]

Solved it. Now let me write it readably and upload it.

ILC

(Ignore vectors and use components when working in 2-space. However, vectors must be used when working in 3-space.)

[ILC]

Here you go, Shawn. It looks like homework so I am going to let you solve the math (use the four equations I gave you).

http://web.syr.edu/~gjhoofna/scan.jpg

ILC

[ShawnD1]

I've already gotten that far but I can't solve for it. I'm trying to remember how matricies work.....

[ILC]

Here:

BC = ABsin(40)/cos(20)

Now, use that equation to solve for AB by plugging into the equation:
ABcos(40) = 490N + BCsin(20)

Plug the answer for AB back into equation 1 to solve for BC.

Plug BC into the equation BCcos(20) = CDcos(60).

Finally, use BC and CD to solve for E.

There, I did your homework for you.

ILC

P.S. Divide E by 9.8 to get the mass.

[ShawnD1]

How do you know all this? Are you in mech eng as well?