What is the length of an arc in a circle with a radius of 10 feet that is subtended by an angle of 81 degrees?

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Calculating the Length of an Arc

The length of an arc in a circle can be calculated using the formula:

Arc Length (L) = (θ/360) × (2 × π × r)

Where:

  • θ = the central angle in degrees
  • r = the radius of the circle
  • π (Pi) ≈ 3.14159

In this case, the radius (r) is given as 10 feet and the angle (θ) is 81 degrees. Now, let’s plug in these values into the formula:

L = (81/360) × (2 × π × 10)

First, we need to calculate the circumference of the circle, which is:

C = 2 × π × r = 2 × π × 10 = 20π

Now, substitute the values into the arc length formula:

L = (81/360) × (20π)

Now, calculate the fraction:

L = (81 × 20π) / 360

This simplifies to:

L = (1620π) / 360 = (9π) / 2

Finally, we can approximate the value of the arc length:

L ≈ 14.1372

So, the arc length of a circle with a radius of 10 feet subtended by an angle of 81 degrees is approximately 14.14 feet.

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