Answer and Step-by-step explanation:
You are correct in that we need to use the Law of Sines: [tex]\frac{c}{sinC} =\frac{b}{sinB}=\frac{a}{sinA}[/tex].
Here, when we use the Law of Sines, we have: [tex]\frac{28}{sin(63)}=\frac{29}{sinB}[/tex].
Cross multiply:
(sinB) * 28 = (sin63) * 29
28sinB ≈ 25.839
sinB ≈ 0.9228
Now, in order to solve for B, we need to use inverse sin ([tex]sin^{-1}[/tex]):
[tex]sin^{-1}(sinB)=sin^{-1}(0.9228)[/tex]
The sines on the left cancel out, and we're left with:
B ≈ 67.3 degrees
Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:
180 - 67.3 = 112.7 degrees.
Hope this helps!
