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

User Nathan Mills
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1 Answer

21 votes
21 votes

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}

User TonyM
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