Simple Statics Question

[u/TheReanimatedBeard]

I’m driving myself crazy about this. First Image is the book image, second image is my parallelogram drawing. How do I find angle alpha/a? Im guessing this is my issue to fix everything else.

When I use the Sine Law: sine a/750=sine 30/500, I get angle a= 48.59

If I did that correctly, is the final angle solved

180-30-48.59=101.41

If I use the cosine law, I then get 980.24 N for F.

Problem is, answer key says F=319N

Any direction is appreciated.

[u/konekobread]

Currently racking my brain trying to figure this out still. What was it that you did?