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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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Math
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2021-10-06T23:05:36+00:00
2021-10-06T23:05:36+00:00 1 Answer
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## Answers ( )

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