What is the length of the arc in a circle with a radius of 3 meters that corresponds to a 30-degree angle?

To calculate the length of the arc (L) in a circle, you can use the formula:

L = (θ / 360) * 2πr

Where:

  • L = length of the arc
  • θ = angle in degrees
  • r = radius of the circle
  • π (pi) = approximately 3.14159

In this case:

  • θ = 30 degrees
  • r = 3 meters

Now, substituting the values into the formula:

L = (30 / 360) * 2π * 3

First, simplify (30 / 360):

  • This simplifies to (1 / 12).

So now the formula looks like:

L = (1 / 12) * 2π * 3

Next, calculate 2π * 3:

  • This results in approximately 18.8496 (since 2π is about 6.2832).

Now plug this value back into our equation:

L = (1 / 12) * 18.8496

Calculating this gives:

  • L ≈ 1.5708 meters

Therefore, the length of the arc subtended by a 30-degree angle in a circle with a radius of 3 meters is approximately 1.57 meters.

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