At first, let us find the measure of angle B
The sum of angles of a triangle is 180 degrees
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ 68+55+m\angle B=180 \\ 123+m\angle B=180 \end{gathered}[/tex]Subtract 123 from both sides to fin m < B
[tex]\begin{gathered} 123-123+m\angle B=180-123 \\ m\angle B=57 \end{gathered}[/tex]Now, let us use the sin rule
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Since b = 42, then
[tex]\frac{a}{\sin68}=\frac{42}{\sin 57}[/tex]By using cross multiplication
[tex]a\sin 57=42\sin 68[/tex]Divide both sides by sin 57
[tex]\begin{gathered} a=\frac{42\sin 68}{\sin 57} \\ a=46.43267974 \\ a=46.4 \end{gathered}[/tex]Do the same to find c
[tex]\frac{42}{\sin57}=\frac{c}{\sin 55}[/tex]By using cross multiplication
[tex]c\sin 57=42\sin 55[/tex]Divide both sides by sin 57
[tex]\begin{gathered} c=\frac{42\sin 55}{\sin 57} \\ c=41.02252681 \\ c=41.0 \end{gathered}[/tex]