1 Answer

Sandrew · Answer 1 · 2023-10-25T16:55:27+0000

To determine the radius of the circle using the portion shown in the picture you have to use the formula to calculate the arc length of the segment.

$s=2\pi r((\theta)/(360))$

Where

s is the arc length

r is the radius

π is the number pi

θ is the central angle

For the portion of the circle shown in the picture, the arc length is s=15cm and the angle is θ=27º

The first step you have to write the formula in terms of r:

$s=2\pi r((\theta)/(360º))$

-Divide both sides by 2π

$\begin{gathered} (s)/(2\pi)=(2\pi)/(2\pi)r((\theta)/(360)) \\ (s)/(2\pi)=r((\theta)/(360)) \end{gathered}$

-Multiply both sides of the expression by the reciprocal fraction of (θ/360), which is (360/θ)

$(s)/(2\pi)\cdot(360)/(\theta)=r$

Next, replace the formula with the given arc length and angle and calculate the radius:

$\begin{gathered} r=(s)/(2\pi)\cdot(360)/(\theta) \\ r=(15)/(2pi)\cdot(360)/(27) \\ r=31.8\operatorname{cm} \end{gathered}$

The radius has a measure of 31.8cm

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