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Answer :
To find the length of an intercepted arc in a circle, we use the formula:
[tex]\[ \text{Arc Length} = \text{Central Angle (in radians)} \times \text{Radius} \][/tex]
The problem gives us the central angle in radians, which is [tex]\(\frac{5\pi}{6}\)[/tex]. We need to calculate the arc length for each given radius: 33.4 inches, 35.6 inches, 37.5 inches, and 39.3 inches. Let's calculate the arc lengths for each of these radii.
a. Radius = 33.4 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 33.4 \][/tex]
[tex]\[ \text{Arc Length} \approx 87.44 \text{ inches} \][/tex]
b. Radius = 35.6 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 35.6 \][/tex]
[tex]\[ \text{Arc Length} \approx 93.20 \text{ inches} \][/tex]
c. Radius = 37.5 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 37.5 \][/tex]
[tex]\[ \text{Arc Length} \approx 98.17 \text{ inches} \][/tex]
d. Radius = 39.3 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 39.3 \][/tex]
[tex]\[ \text{Arc Length} \approx 102.89 \text{ inches} \][/tex]
Therefore, the lengths of the intercepted arcs for each radii are approximately 87.44 inches, 93.20 inches, 98.17 inches, and 102.89 inches, respectively.
[tex]\[ \text{Arc Length} = \text{Central Angle (in radians)} \times \text{Radius} \][/tex]
The problem gives us the central angle in radians, which is [tex]\(\frac{5\pi}{6}\)[/tex]. We need to calculate the arc length for each given radius: 33.4 inches, 35.6 inches, 37.5 inches, and 39.3 inches. Let's calculate the arc lengths for each of these radii.
a. Radius = 33.4 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 33.4 \][/tex]
[tex]\[ \text{Arc Length} \approx 87.44 \text{ inches} \][/tex]
b. Radius = 35.6 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 35.6 \][/tex]
[tex]\[ \text{Arc Length} \approx 93.20 \text{ inches} \][/tex]
c. Radius = 37.5 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 37.5 \][/tex]
[tex]\[ \text{Arc Length} \approx 98.17 \text{ inches} \][/tex]
d. Radius = 39.3 inches
Using the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 39.3 \][/tex]
[tex]\[ \text{Arc Length} \approx 102.89 \text{ inches} \][/tex]
Therefore, the lengths of the intercepted arcs for each radii are approximately 87.44 inches, 93.20 inches, 98.17 inches, and 102.89 inches, respectively.
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