The arc length of an arc subtended by an angle measuring 11π/18 radians is 78.6 inches. What is the radius of the arc?

Question

The arc length of an arc subtended by an angle measuring 11π/18 radians is 78.6 inches.

What is the radius of the arc?

approximately 36.5 inches

approximately 40.9 inches

approximately 48.0 inches

approximately 128.6 inches

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Adalynn 1 week 2021-10-06T23:05:36+00:00 1 Answer 0

Answers ( )

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    2021-10-06T23:07:28+00:00

    Answer: approximately 40.9 inches

    Step-by-step explanation:

    The formula for determining the length of an arc is expressed as

    Length of arc = θ/360 × 2πr

    Where

    θ represents the central angle.

    r represents the radius of the circle.

    π is a constant whose value is 3.14

    From the information given,

    θ = 11π/18

    2π = 360 degrees

    π = 360/2 = 180

    Therefore,

    θ = 11 × 180/18 = 110 degrees

    Length of arc = 78.6 inches

    Therefore,

    78.6 = 110/360 × 2 × 3.14 × r

    78.6 = 1.919r

    r = 78.6/1.918888

    r = 40.9 inches

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