First, let's draw a picture of the triangle:
From the law of sines, we have that
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
So,we can to find angle B, that is,
[tex]\frac{48.35}{sin18.92}=\frac{105}{sinB}[/tex]
which gives
[tex]sinB=\frac{105sin18.92}{48.35}[/tex]
then
[tex]sinB=0.70415[/tex]
so we have
[tex]B=sin^{-1}0.70415=44.761499[/tex]
Since interior angles add up to 180, we have that
[tex]\angle C+\angle A+\angle B=180[/tex]
which gives
[tex]\angle C+18.92+44.761499=180[/tex]
Then, angle C is given as
[tex]\begin{gathered} \angle C=180-116.3185 \\ \angle C=116.3185 \end{gathered}[/tex]
Once we have obtained angle C, we can to find side c by substituting the last result into the law of sine from above
[tex]\frac{b}{sinB}=\frac{c}{sinC}\Rightarrow\frac{105}{sin44.761499}=\frac{c}{sin116.3185}[/tex]
which implies that
[tex]c=\frac{105sin116.3185}{sin44.761499}[/tex]
it yields
[tex]c=\frac{94.1116}{0.70415}=133.659[/tex]
Therefore, by rounding to the nearest tenths, the answer is 133.7 yards
