Answer :
To find the length of the intercepted arc with a given central angle and radius, you can use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Here's how we can solve the problem step-by-step:
1. Identify the given values:
- The radius of the circle, [tex]\( r \)[/tex], is 15 inches.
- The central angle, [tex]\( \theta \)[/tex], is given as [tex]\( \frac{5\pi}{6} \)[/tex] radians.
2. Apply the arc length formula:
[tex]\[
\text{Arc Length} = 15 \times \frac{5\pi}{6}
\][/tex]
3. Calculate the arc length:
- Multiply the radius by the central angle in radians:
[tex]\[
\text{Arc Length} = 15 \times \frac{5\pi}{6} = 15 \times 2.61799 \approx 39.27 \text{ inches}
\][/tex]
4. Select the closest answer:
- Looking at the options, the closest value to our calculated arc length is approximately 39.3 inches.
Therefore, the best answer is:
[tex]\[ \text{d. 39.3 inches} \][/tex]
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Here's how we can solve the problem step-by-step:
1. Identify the given values:
- The radius of the circle, [tex]\( r \)[/tex], is 15 inches.
- The central angle, [tex]\( \theta \)[/tex], is given as [tex]\( \frac{5\pi}{6} \)[/tex] radians.
2. Apply the arc length formula:
[tex]\[
\text{Arc Length} = 15 \times \frac{5\pi}{6}
\][/tex]
3. Calculate the arc length:
- Multiply the radius by the central angle in radians:
[tex]\[
\text{Arc Length} = 15 \times \frac{5\pi}{6} = 15 \times 2.61799 \approx 39.27 \text{ inches}
\][/tex]
4. Select the closest answer:
- Looking at the options, the closest value to our calculated arc length is approximately 39.3 inches.
Therefore, the best answer is:
[tex]\[ \text{d. 39.3 inches} \][/tex]