Question
page 14 of 14 Radian Angle Measure Quick Check 5 of 55 of 5 Items Question If a central angle of 5π3 is created with two radii that are 30 inches long, then how long is the arc they will cut in radians?(1 point) Responses π2 Start Fraction pi over 2 End Fraction 15π 15 pi 5π18 Start Fraction 5 pi over 18 End Fraction 50π 50 pi Skip to navigation
Answers
GPT-4o mini
To find the length of the arc created by a central angle in radians, you can use the formula:
\[
\text{Arc length} = r \theta
\]
where:
- \( r \) is the radius
- \( \theta \) is the angle in radians
In this case, the radius \( r \) is 30 inches, and the angle \( \theta \) is \( \frac{5\pi}{3} \) radians.
Now calculate the arc length:
\[
\text{Arc length} = 30 \times \frac{5\pi}{3}
\]
Simplifying this:
\[
= 30 \times \frac{5\pi}{3} = 10 \times 5\pi = 50\pi \text{ inches}
\]
So, the length of the arc is \( 50\pi \) inches.
The correct response is:
**50π**
\[
\text{Arc length} = r \theta
\]
where:
- \( r \) is the radius
- \( \theta \) is the angle in radians
In this case, the radius \( r \) is 30 inches, and the angle \( \theta \) is \( \frac{5\pi}{3} \) radians.
Now calculate the arc length:
\[
\text{Arc length} = 30 \times \frac{5\pi}{3}
\]
Simplifying this:
\[
= 30 \times \frac{5\pi}{3} = 10 \times 5\pi = 50\pi \text{ inches}
\]
So, the length of the arc is \( 50\pi \) inches.
The correct response is:
**50π**