To find the length of the arc, we can use the formula:
Arc Length = (θ / 360) × 2πr
where:
- θ is the angle in degrees (70 degrees in this case)
- r is the radius of the circle (6 inches)
- π is a constant (approximately 3.14159)
Now, substituting the values into the formula:
Arc Length = (70 / 360) × 2π × 6
First, simplify (70 / 360):
(70 / 360) = 0.1944 (approximately)
Now, plug that back into the equation:
Arc Length = 0.1944 × 2 × 3.14159 × 6
Calculating that gives:
Arc Length ≈ 0.1944 × 37.6991 ≈ 7.33 inches
Therefore, the length of the arc subtended by an angle of 70 degrees in a circle with a radius of 6 inches is approximately 7.33 inches.