Answer:
9.77 ft.
Explanation:
To find the length of the radius, we can use the formula for the area of a sector:
Area = (π * r^2 * θ) / 360
Given that the sector area is 126.7 ft² and the central angle is 120°, we can substitute these values into the formula and solve for the radius.
126.7 = (π * r^2 * 120) / 360
To simplify the equation, we can cancel out the common factor of 120:
126.7 = (π * r^2) / 3
Next, we can multiply both sides of the equation by 3 to isolate the term with r^2:
380.1 = π * r^2
Finally, we can solve for r by dividing both sides of the equation by π and taking the square root:
r^2 = 380.1 / π
r ≈ √(380.1 / π)
Using a calculator, we can find that the approximate value of the radius, r, is approximately 9.77 ft.
Therefore, the length of the radius is approximately 9.77 ft.
I hope this explanation helps you understand how to find the length of the radius in this scenario. If you have any further questions, feel free to ask.