Questions: Use the arc constant to determine the length of the arcs given the measurement of the radius. Round answers to the nearest 1/16": Arc length = Arc length =

Use the arc constant to determine the length of the arcs given the measurement of the radius. Round answers to the nearest 1/16": Arc length = Arc length =
Transcript text: Use the arc constant to determine the length of the arcs given the measurement of the radius. Round answers to the nearest $\frac{1}{16}$ ": Arc length $=$ Arc length $=$
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Solution

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Solution Steps

Step 1: Find the central angle in radians for part a.

The central angle is 1 degree. To convert to radians, we multiply by π/180: 1 * (π/180) = π/180 radians.

Step 2: Calculate the arc length for part a.

Arc length is given by the formula s = rθ, where r is the radius and θ is the central angle in radians. s = 7 * (π/180) ≈ 0.122 inches.

Step 3: Convert the arc length in part a to the nearest 1/16 inch.

0.122 inches is approximately 2/16 = 1/8 inch.

Step 4: Find the central angle in radians for part b.

The central angle is 3 degrees. To convert to radians, we multiply by π/180: 3 * (π/180) = 3π/180 = π/60 radians.

Step 5: Calculate the arc length for part b.

Arc length is given by the formula s = rθ, where r is the radius and θ is the central angle in radians. s = 8 * (π/60) ≈ 0.419 inches.

Step 6: Convert the arc length in part b to the nearest 1/16 inch.

0.419 inches is approximately 7/16 inch since (7/16) is equal to 0.4375 inches.

Final Answer:

a. Arc length = 1/8" b. Arc length = 7/16"

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