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How do you find the radian measure of the central angle of a circle of r = 4" that intercepts an arc length s = 20"?

Answer 1

Samantha Abate

A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius.

So:

#alpha_(rad)=(arc)/r#

#alpha_(rad)=20/4=5rad#.

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Answer 2

Quinn Anderson

To find the radian measure of the central angle of a circle with radius ( r = 4 ) inches intercepting an arc length ( s = 20 ) inches, you can use the formula:

[ \text{Radian measure of central angle} = \frac{s}{r} ]

Substituting the given values:

[ \text{Radian measure of central angle} = \frac{20}{4} = 5 , \text{radians} ]

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