SAS with Laws of Sine and Cosine

Hello. I had to solve the following triangle using Law of Sines / Cosines:

b = 6

c = 13

alpha = 16 degrees

The first time I solved the triangle, I first used the law of cosines and got

a = 7.42

I then used the law of sines to solve for beta and got 12.9 degrees. (beta = sin inverse of 6 sin 16 / 7.42)

I then used 180 - (16 + 12.9) and found gamma to be 151.1 degrees.

I then solved the triangle a second time, but instead of solving for the beta angle using the law of sines, I solved for gamma.

In that case, I found that gamma was equal to 28.8 degrees. (gamma = sin inverse of 13 sin 16 / 7.42) This would then make beta equal to 135.2 degrees.

I read that I'm supposed to solve for the smaller angle first using the law of sines. Can solving for the larger angle first cause such a wide variation in the answer, or did I incorrectly solve for the larger angle?

Thanks!