Question

In circle B with mLABC = 36 and AB = 3 units, find the length of arc AC. Round to the nearest hundredth. С B

Answer 1

We want to find the length of arc AC in the given figure.

Given;

$\begin{gathered} m\angle ABC=\theta=36^{\circ} \\ AB=r=3\text{ units} \end{gathered}$

Recall that the length of an arc can be calculated using the formula;

$l=\frac{\theta}{360}\times2\pi r$

Substituting the given values;

$\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ AC=\frac{36}{360}\times2\pi(3) \\ AC=\frac{1}{10}\times6\pi \\ AC=1.88\text{ units} \end{gathered}$

Therefore, the length of the arc AC is;

$1.88\text{ units}$