How can I solve for beta and gamma in a cartesian vector addition problem?

[whynot314]

I am having a really tough time trying to solve this particular problem I can find alpha easily 139 degrees which is correct. However when I go to try and solve for beta or gamma I get this huge mess and I am unable to solve for either one, Please help me I know I am overlooking something but I don't know what it is.

[URL=http://s1341.photobucket.com/user/nebula-314/media/20130623_203154_zpsc06ba2e7.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130623_203154_zpsc06ba2e7.jpg[/URL][/PLAIN]

 

[Simon Bridge]

You need to show your reasoning, not just a sheet full of symbols and numbers.