If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81 degrees?

To find the length of the arc subtended by an angle in a circle, we can use the formula:

Arc Length = (θ / 360) × 2πr

Where:

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

In this case, the radius (r) is 10 feet, and the angle (θ) is 81 degrees. Plugging these values into the formula gives us:

Arc Length = (81 / 360) × 2π × 10

Now, let’s calculate it step by step:

1. First, calculate 2π × 10:
   2 × 3.14159 × 10 = 62.8318
2. Next, find (81 / 360):
   81 / 360 ≈ 0.225
3. Now, multiply them together:
   Arc Length = 0.225 × 62.8318 ≈ 14.14 feet

So, the arc length is approximately 14.14 feet.