Solution to 'Simple' Trig Problem

Ok, this took me ages to figure out, trying various methods and stuff and getting all messed up. I even had to get help from David himself, who seemed to know a formula that I didn't but was expected to know for this question. Fine, so I fail at basic trig. Maybe I just suck, I'm no match for evil IB HL people.

Anyway, this is a diagram (which I'm hoping real hard that it's right)




Erm... The answer I got at the end was approximately 10.88, please tell me if this is right or wrong and therefore whether I should bother showing what I did.

Cheers.