A circle has a radius of 13 ft. What is the LENGTH of an arc of that circle that is captured by a central angle that measures 112 degrees? Round your answer to the nearsest hundredth
To find the length of the arc, we can use the formula:
Arc Length = 2πr (θ/360)
where r is the radius of the circle, θ is the central angle in degrees, and π is approximately 3.14.
In this case, r = 13 ft and θ = 112 degrees. Plugging these values into the formula:
Arc Length = 2π(13) (112/360)
Arc Length = 26π (0.3111)
Arc Length ≈ 26 * 3.14 * 0.3111
Arc Length ≈ 25.925 ft
Therefore, the length of the arc of the circle captured by a central angle of 112 degrees is approximately 25.93 ft.