High School

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------------------------------------------------ A circle has a radius of 17 cm. Find the length \( s \) of the arc intercepted by a central angle of 66 degrees.

Answer :

Arc length (s) = radius (r) x θ (in radians)

First, convert 66° into radians using the proportion π = 180°
[tex] \frac{ \pi}{180} = \frac{x}{66} [/tex]
[tex] \frac{66 \pi }{180} = x[/tex]
[tex] \frac{11 \pi }{30} = x[/tex]

s = r θ
= 17 ([tex] \frac{11 \pi }{30}[/tex])
= [tex] \frac{187 \pi }{30} [/tex]

Answer: [tex] \frac{187 \pi }{30} [/tex] ≈ 19.6 cm
Circumference = 2*17 pi = 34pi cms

length of s = (66/360) * 34 pi = 6.233 pi = 19.58 cm to nearest hundredth

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