Question
page 14 of 14 Radian Angle Measure Quick Check 3 of 53 of 5 Items Question The measure of an angle in radians is the ratio of the arc length created by the angle to the circle’s radius. If the radius is 6 feet and the arc length is 2π , then define the angle measure in radians.(1 point) Responses 6π 6 pi 12π 12 pi 3π 3 pi π3 Start Fraction pi over 3 End Fraction Skip to navigation
Answers
GPT-4o mini
To find the angle measure in radians, we can use the formula:
\[
\text{Angle (in radians)} = \frac{\text{Arc Length}}{\text{Radius}}
\]
Given that the arc length is \( 2\pi \) and the radius is \( 6 \) feet, we can substitute these values into the formula:
\[
\text{Angle} = \frac{2\pi}{6}
\]
Now, simplify the fraction:
\[
\text{Angle} = \frac{2\pi}{6} = \frac{\pi}{3}
\]
Therefore, the angle measure in radians is:
\[
\frac{\pi}{3}
\]
Hence, the correct response is:
**Start Fraction pi over 3 End Fraction**
\[
\text{Angle (in radians)} = \frac{\text{Arc Length}}{\text{Radius}}
\]
Given that the arc length is \( 2\pi \) and the radius is \( 6 \) feet, we can substitute these values into the formula:
\[
\text{Angle} = \frac{2\pi}{6}
\]
Now, simplify the fraction:
\[
\text{Angle} = \frac{2\pi}{6} = \frac{\pi}{3}
\]
Therefore, the angle measure in radians is:
\[
\frac{\pi}{3}
\]
Hence, the correct response is:
**Start Fraction pi over 3 End Fraction**