To solve the exercise you can use the cosine law, which applies to any triangle, its formula is
[tex]a^2=-2bc\cos (A)+b^2+c^2[/tex]
So, in this case, you have
[tex]\begin{gathered} a^2=-2bc\cos (A)+b^2+c^2 \\ a^2=-2(8)(13)\cos (89)+(8)^2+(13)^2 \\ a^2=229 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{a^2}=\sqrt[]{229.37} \\ a=15.1 \end{gathered}[/tex]
Therefore, the missing side measurement is 15.1 units.
