To calculate the length of the arc on a circle that is intercepted by a central angle, you can use the formula:
Arc Length (L) = r × θ
Where:
- L = Length of the arc
- r = Radius of the circle
- θ = Central angle in radians
However, in your case, the central angle is given in degrees (8 degrees). To use the formula, you need to convert the angle from degrees to radians. The conversion from degrees to radians can be done using the formula:
Radians = Degrees × (π / 180)
So, for an angle of 8 degrees:
θ = 8 × (π / 180) = (8π / 180) = (2π / 45) radians
Now, you can substitute this back into the arc length formula:
L = r × (2π / 45)
This means that the length of the arc (L) is:
L = (2πr) / 45
Now, simply plug in the value of the radius (r) to find the length of the arc corresponding to your central angle of 8 degrees.
For example, if the radius r = 5 units, then:
L = (2π × 5) / 45 = (10π) / 45 = (2π) / 9 units
This is how you would find the length of the arc intercepted by a central angle of 8 degrees on a circle of radius r.