Answer:
The value that best approximates the radius of the circle is 13.43 inches.
The arc length of a circle is given by the formula L = rθ where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
Since we are given that the central angle measures 64° and that the arc intercepted by this central angle measures 15 inches, we can convert 64° to radians by multiplying it by π/180.
Therefore, θ = (64π)/180.
We can then solve for r using L = rθ and substituting L = 15 inches and θ = (64π)/180. This gives us r ≈ 13.43 inches.
Therefore, 13.43 in best approximates the radius of the circle.