Find the radius of a circle in which the central​ angle, a, intercepts an arc of the given length s. a = 156°, s = 25 km

Question

Find the radius of a circle in which the central​ angle, a, intercepts an arc of the given length s. a = 156°, s = 25 km

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Everleigh 3 weeks 2021-09-08T13:03:33+00:00 1 Answer 0

Answers ( )

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    2021-09-08T13:04:58+00:00

    Answer:

    Radius of the circle is 9.178

    Step-by-step explanation:

    Given that,

    Central angle ,a = 156°

    Arc length,s =25 km

    The formula to calculate the radius of a circle is;  

    Arc length= Θ / 360° x  (2πr)

    We are given that the Θ =20° and that arc length is 66 in. Substituting, we have;

    L = Θ / 360°  x (2πr)

    25 = (156  / 360°) x 2 x 22/7 x r

    25 = 6864r / 2520

    r= (2520 x 25) / 6864

    r= 63000 / 6864

    r =  9.178

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