A circles has radius 10 centimeters. Suppose an arc on the circle has length 8\pi centimeters. what is the measure of the central

Question

A circles has radius 10 centimeters. Suppose an arc on the circle has length 8\pi centimeters. what is the measure of the central angle whose radii define the arc?

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Thu Thủy 4 years 2021-08-06T21:40:20+00:00 1 Answers 308 views 0

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  1. RuslanHeatt
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    2021-08-06T21:41:52+00:00
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    Answer:

    The measure of the central angle whose radii define the arc is \mathbf{\frac{4\pi }{5} }

    Step-by-step explanation:

    Radius of circle = 10 cm

    Length of arc = 8\pi

    We need to find Theta \theta

    The formula used will be: S=r \theta

    S= length of arc, r = radius and \theta = angle

    Putting values and finding \theta

    S=r \theta\\8\pi =10 \theta\\\theta=\frac{8\pi }{10} \\\theta=\frac{4\pi }{5}

    So, the measure of the central angle whose radii define the arc is \mathbf{\frac{4\pi }{5} }

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