Since we are given a pair and need to find the side of another pair, we use the sine rule.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
One pair is
38 degree angle and opposite side of 13
Another pair [to solve] is
110 degree angle and side 'b' to solve
We substitute into the formula:
[tex]\frac{13}{\sin38}=\frac{b}{\sin 110}[/tex]
We can cross multiply and solve for b. The process is shown below:
[tex]\begin{gathered} 13\times\sin 110=b\times\sin 38 \\ b=\frac{13\sin 110}{\sin 38} \\ b=19.84 \end{gathered}[/tex]
The measure of side b of the triangle shown:
19.84
