Length of an Arc
<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-length-of-an-arc" target="_blank">Length of an Arc Exercise</a></p><p>To find the <strong><span style="color:#8e44ad;">Length of an Arc</span></strong>, first recognize that an entire circle's circumference corresponds to $360$°.</p>
<p>So, to find a piece of that circumference (also known as an arc), we simply have to use its central angle and set up a proportion.</p>
<p><strong><span style="color:#27ae60;">Example</span></strong></p>
<p>What is the length of the arc below?</p>
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<p><strong><span style="color:#27ae60;">Set Up the Proportion and Solve</span></strong></p>
<p>$$\frac{central \ angle}{360} = \frac{arc}{circumference}$$</p>
<p>$$\frac{75}{360} = \frac{arc}{2 \pi r}$$</p>
<p>$$\frac{75}{360} = \frac{arc}{12\pi}$$</p>
<p>$$12\pi \times 75 = 360 \times arc$$</p>
<p>$$\frac{(12\pi)(75))}{360} = arc$$</p>
<p><span style="color:#27ae60;">$$arc = 2.5\pi$$</span></p>
<p>Whew.</p>