The radius of the circle is approximately 5.95 inches.
Here's how you can solve it:
Formula: We know that the arc length (s) of a circle is related to the central angle (θ) and the radius (r) by the formula:
s = (θ/360°) * 2πr
Plugging in values: In this case, you know the arc length (s) is 9.42 inches and the central angle (θ) is 90 degrees (since ACB is a right angle). We need to solve for the radius (r).
9.42 inches = (90°/360°) * 2πr
Solving for r: Isolate r by dividing both sides by (θ/360°) and 2π:
r = 9.42 inches / ((90°/360°) * 2π)
Calculating r: Simplify the expression and round the answer to 3 significant figures:
r ≈ 9.42 inches / (0.25 * 6.2832)
r ≈ 5.95 inches (rounded to 3 significant figures)
Therefore, the radius of the circle is approximately 5.95 inches.