Answer :
We want to find the length of arc AC in the given figure.
Given;
[tex]\begin{gathered} m\angle ABC=\theta=36^{\circ} \\ AB=r=3\text{ units} \end{gathered}[/tex]Recall that the length of an arc can be calculated using the formula;
[tex]l=\frac{\theta}{360}\times2\pi r[/tex]Substituting the given values;
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ AC=\frac{36}{360}\times2\pi(3) \\ AC=\frac{1}{10}\times6\pi \\ AC=1.88\text{ units} \end{gathered}[/tex]Therefore, the length of the arc AC is;
[tex]1.88\text{ units}[/tex]