Do not round (or round to 4 decimal places) until you get to the end. This is where your error is coming from.
I have an issue solving the following problem. This starts using the law of cosines. Anyway, given the following, solve the triangle
side a = 12
b = 5
c = 13
law of cosines is which yields me an angle B of 23 degrees, so far so good.
so next you're supposed to use the law of sines to solve for the next angle. I'm solving for A for the hell of it, so I get
or
that gives me A = 69degrees...but according to the book, it's 67 degrees.
and if I solve for C instead, I get
or
and that doesn't even work, since the left hand of the equation is great than 1, it's out of domain or whatever.
So...what am I doing wrong?