Question

the central angle of an arc is 2.84 radians. the radius of the circle is 20. find the length of the arc.
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an arc subtends a central angle of $\frac{13}{9}pi$ radians. what fraction of the circumference is the arc?
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Explanation:

Step1: Recall arc length formula

The formula for arc length $s$ is $s = r\theta$, where $r$ is radius, $\theta$ is central angle in radians.

Step2: Substitute given values

$r=20$, $\theta=2.84$.
$s = 20 \times 2.84$

Step3: Calculate the arc length

$s = 56.8$

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Step1: Recall full circle angle

A full circle has a central angle of $2\pi$ radians.

Step2: Find the fraction

Fraction = $\frac{\text{arc's central angle}}{\text{full circle angle}}$
Fraction = $\frac{\frac{13}{9}\pi}{2\pi}$

Step3: Simplify the fraction

Cancel $\pi$: $\frac{\frac{13}{9}}{2} = \frac{13}{9} \times \frac{1}{2} = \frac{13}{18}$

Answer:

1. $56.8$
2. $\frac{13}{18}$