To find the length of an arc in a circle, you can use the formula:
Arc Length = (θ / 360) × (2πr)
Where:
- θ is the angle in degrees (in this case, 45 degrees)
- r is the radius of the circle (in this case, 8)
Now, plug in the values:
Arc Length = (45 / 360) × (2π × 8)
Simplifying the fraction:
45 / 360 = 1 / 8
So the formula becomes:
Arc Length = (1 / 8) × (2π × 8)
Now, calculate:
Arc Length = (1 / 8) × (16π) = 2π
Now, substituting the value of π (approximately 3.14):
Arc Length = 2 × 3.14 = 6.28
Thus, the length of the arc is approximately 6.28 units.