Law of Sines

sigma=27 deg 30'
c= 52.8
a=28.1

Please show two solutions (beta1, beta2,...) due to acute and obtuse angles.

Thank you so much for helping!

No idea which angle sigma is, but I'll assume it's C, since otherwise you'd probably have used alpha.

sinA/a = sinC/c
so,
sinA/28.1 = .4617/52.8
sinA = .2457
A = 14.2° or 165.3°

Now you can find B and b.