Question
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
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Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
The length of the arc of a circle with a radius of 13 ft, captured by a central angle of 112 degrees, is approximately 25.93 ft. The calculation involves using the formula for arc length, which considers the radius of the circle and the measure of the central angle in degrees. In this case, the formula yielded an arc length of 26π (0.3111), which, when calculated, translates to the rounded answer of 25.93 ft.
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