Final answer:
To find the radius, convert the central angle to radians and use As = rA. The radius computes to approximately 12.8 inches, but this doesn't match the provided answer options, suggesting re-evaluation or a possible typo in the question or answers.
Step-by-step explanation:
The student is asking to find the radius of a circle given the measure of the central angle and the arc length. The arc length is a portion of the circumference of the circle, and the central angle is the angle subtended by the arc at the center of the circle. The relationship between the arc length (As), the central angle in radians (A), and the radius (r) of the circle is given by the formula As = rA. Since we are dealing with degrees, we need to convert the central angle to radians before using the formula by multiplying the degree measure by π/180.
First convert the central angle to radians: A = 45° * (π/180) = π/4 radians.
Then use the formula to find the radius: As = rA, rearranging we get r = As/A.
So, r = 10 inches / (π/4) = 40 inches / π ≈ 12.7 inches which we round to 12.8 inches, but none of the provided options match this computed value. Make sure to double-check the provided options and calculations.