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=(\theta)/(360)*2\pi r`

Substituting the given values;

`\begin{gathered} l=(\theta)/(360)*2\pi r \\ AC=(36)/(360)*2\pi(3) \\ AC=(1)/(10)*6\pi \\ AC=1.88\text{ units} \end{gathered}`

Therefore, the length of the arc AC is;

`1.88\text{ units}`