To find the arc length using the arc length formula, we first need to know the relationship between the angle, the radius, and the arc length. The formula for the arc length (s) is given by:
s = r * θ
Where:
- s is the arc length.
- r is the radius of the circle.
- θ is the angle in radians.
In this case, we are given:
- s = 8 meters
- r = 12 meters
- θ = 8 radians
To find the arc length corresponding to the angle of 8 radians with a radius of 12 meters, we substitute the values into the formula:
s = 12 m * 8 rad
Calculating this gives:
s = 96 meters
Thus, the arc length is 96 meters. This method of using the arc length formula is straightforward once you have the radius and the angle in radians, making it easy to determine the length of any arc in a circle.