I'm currently cramming for a statics final, and it seems that I understand all of the concepts but lack the fundamental geometry skills to tie it all together.

In a basic problem such as this:

http://s1303.photobucket.com/user/Tr...6xyy9.png.html
The goal is to find the the resultant forces. I get the plan: divide each force into 3 components and figure out the magnitude in each direction, then figure out the resultant.

I first found F1Z, which is simply F1sin(60).

Then I found the random line between F1 and the Y axis with F1cos(60) and denoted it as F'. This is where I was halted.

I'm looking at the solution, and the next step they used -F'cos(45) to find F1 in the X direction. Looking at the picture, it seems -F'cos(45) would give you a force along the Y axis, as cosine finds the adjacent side. What am I missing here?

Also, as a side note, what exactly is F'? I've been using it to this point without actually understanding what it is in the grand scheme of things.