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 A central angle with measure 120 degrees is drawn in a circle with a circumference of 8 pi miles. What is the length of the intercepted arc, rounded to the tenth of a mile?

frowncrying

 May 24, 2017
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\(\frac{\text {arc length}}{\text{circumference of circle}}=\frac{120^{\circ}} {360^{\circ}} \\~\\ \frac{\text{arc length}}{8\pi}=\frac{120^{\circ}} {360^{\circ}} \\~\\ \begin{array} \ \text{arc length}&=&\frac{120^{\circ}} {360^{\circ}}*8\pi \\~\\ &=&\frac13*8\pi \\~\\ &=& \frac{8\pi}{3} \\~\\ &\approx& 8.4 \, \text{miles} \end{array}\)

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 May 24, 2017

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