Question

If the circumference of a circle is 24, and the angle measure of an arc is 120°, which is the length of the arc?

Answer 1

Using radian meansure
theta = (arc length)/radius
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arc length = radius*theta
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Your Problem:
120 degrees = 120(pi/180) = (2/3)pi radians

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circumference = 2pi*r
24 = 2pi*r
r = 12/pi
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arc length = (12/pi)(2/3)pi = 8 units

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