To find the central angle of a circle based on the length of the arc, we can use the relationship between the arc length, the radius, and the central angle in radians.
The formula for arc length (L) is given by:
L = r * θ
Where:
- L is the length of the arc
- r is the radius of the circle
- θ is the central angle in radians
In your case, you know:
- The radius r = 4 ft
- The arc length L = 10 ft
Now we can rearrange the formula to solve for the central angle θ:
θ = L / r
Plugging in the values:
θ = 10 ft / 4 ft
θ = 2.5 radians
So, the central angle corresponding to the defined arc of 10ft on a circle with a radius of 4ft is approximately 2.5 radians.