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Answer :
To find the length of the intercepted arc, you can use the formula for arc length in a circle:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Here, we are given:
- Central Angle = [tex]\(\frac{5\pi}{6}\)[/tex] radians
- Radius = 15 inches
Now, substitute these values into the formula:
[tex]\[ \text{Arc Length} = 15 \times \frac{5\pi}{6} \][/tex]
Calculate the arc length:
1. Multiply the radius by the central angle:
[tex]\[ 15 \times \frac{5\pi}{6} = \frac{75\pi}{6} \][/tex]
2. Simplify the fraction:
[tex]\[ \frac{75\pi}{6} = 12.5\pi \][/tex]
3. To get a numerical result, approximate [tex]\(\pi\)[/tex] as 3.1416:
[tex]\[ 12.5 \times 3.1416 \approx 39.27 \][/tex]
Therefore, the arc length is approximately [tex]\( 39.3 \)[/tex] inches. Hence, the best answer from the choices provided is:
D. 39.3 inches
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Here, we are given:
- Central Angle = [tex]\(\frac{5\pi}{6}\)[/tex] radians
- Radius = 15 inches
Now, substitute these values into the formula:
[tex]\[ \text{Arc Length} = 15 \times \frac{5\pi}{6} \][/tex]
Calculate the arc length:
1. Multiply the radius by the central angle:
[tex]\[ 15 \times \frac{5\pi}{6} = \frac{75\pi}{6} \][/tex]
2. Simplify the fraction:
[tex]\[ \frac{75\pi}{6} = 12.5\pi \][/tex]
3. To get a numerical result, approximate [tex]\(\pi\)[/tex] as 3.1416:
[tex]\[ 12.5 \times 3.1416 \approx 39.27 \][/tex]
Therefore, the arc length is approximately [tex]\( 39.3 \)[/tex] inches. Hence, the best answer from the choices provided is:
D. 39.3 inches
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