To find the length of the arc on a circle of radius r that is intercepted by a central angle of 8 degrees, we can use the formula for the arc length.
The formula to calculate arc length (s) is:
s = r × θ
Where:
- s = arc length
- r = radius of the circle
- θ = central angle in radians
First, we need to convert the angle from degrees to radians because the formula requires the angle in radians. The conversion from degrees to radians is done using the formula:
radians = degrees × (π / 180)
So, for our case:
θ = 8 × (π / 180) = (8π / 180) = (2π / 45) radians
Now, substituting this value back into the arc length formula, we get:
s = r × (2π / 45)
This means the length of the arc intercepted by a central angle of 8 degrees in a circle with radius r is:
s = (2πr) / 45
This formula allows you to calculate the arc length for any given radius by simply plugging in the value of r.