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In a circle whose radius measures 6 feet, a central angle intercepts an arc of length 9 feet, how do you find the radian measure of the central angle?

Answer 1

Oliver Atkinson

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)=9/6=1.5rad#.

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Answer 2

Carter Anderson

To find the radian measure of the central angle, we can use the formula relating the arc length, radius, and central angle in a circle:

[ \text{Arc length} = \text{Radius} \times \text{Central angle in radians} ]

Given that the radius of the circle is 6 feet and the arc length is 9 feet, we can plug these values into the formula:

[ 9 = 6 \times \text{Central angle in radians} ]

Solving for the central angle in radians:

[ \text{Central angle in radians} = \frac{9}{6} = \frac{3}{2} ]

Therefore, the radian measure of the central angle is ( \frac{3}{2} ) radians.

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