To find the length of the arc subtended by an angle in a circle, you can use the formula:
Arc Length (L) = (θ / 360) * 2 * π * r
Where:
- L = arc length
- θ = angle in degrees (70 degrees in this case)
- r = radius of the circle (6 inches)
Now, let’s substitute the values into the formula:
L = (70 / 360) * 2 * π * 6
Calculating step by step:
1. Calculate the fraction: 70 / 360 = 0.1944 (approximately)
2. Calculate 2 * π * 6: 2 * 3.14159 * 6 = 37.6991 inches (approximately)
3. Multiply the fraction by the circumference: 0.1944 * 37.6991 ≈ 7.328 inches
The length of the arc is therefore approximately 7.33 inches.