in triangle abc angle a=42 line segment ac=12 and cb=22 what is the measure for angle b

We can use the Law of Sines  to solve this

sin(42) / 22  = sin B / 12

sin B  = 12 sin(42 )/ 22

arcsin [ 12sin(42)/22]  = B  = about 21.41°

Since we have a SSA  situation, we have to check to see if we have another triangle

So....the other possibility for B  = [180 - 21.41] °  = 158.59°

But, this would mean the sum of angles A  and B  would exceed 180°  ....so, we only have one triangle