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.