Here's a link to the website that has the problem. It's right under example 1.
The Attempt at a Solution
This is just for the first part; finding Curly's force.
For the sled not to move up or down, both Curly and Moe will each have to have a y component force that cancels out the other one. I calculated Moe's y component force to be 17.32 N, which means Curly would also have to have 17.32 N of downward force to negate Moe's force. Then I calculated Curly's x component of force from having his y component of force and got 29.999 N of force.
What they did is completely foreign to me. First, they got 8.660 N as Moe's y component of force because they multiplied .866, the sine, times the x component. I don't know why they did that.
Then they just divided the 8.660 they got by Curly's sine to get Curly's x component of force. I don't see why they did that and they don't explain why they were doing it.