Respuesta :
Answer:
arc length = approx. 6/3.14 units
Step-by-step explanation:
Let s represent arc length.
The formula for arc length is thus s = rФ, where Ф is the central angle in radians.
Here we're given the central angle in degrees. We must convert this to radians. The following operations will accomplish that:
72 deg π rad 6 rad
----------- * -------------- = 0 = ----------- = 0.6 rad
1 180 deg 15
We need to evaluate s = rФ, where Ф is the central angle in radians. That works out to be s = r(0.6 rad). We are not given the radius, r, so must calculate it from the known fact that the circumference, C, is 20 units, and that this equals 2π*r. C/(2π) is the radius: 20 units/2π, or 10/π = r.
Returning to s = r(0.6 rad), from above, we get:
s = (10/π)((0.6 rad) = 6/π units, or approx. 6/3.14 units.
The value of the length of the arc for the provided circle with circumference 20 and has an arc with a 72 degree is 8 units.
How to find the length of the arc?
Central angle is the angle which is substended by the arc of the circle at the center point of that circle. The formula which is used to calculate the length of the arc is given below.
[tex]s=r\theta[/tex]
Here, (r) is the radius of the circle, (θ) is the central angle and (s) is the arc length.
A circle with circumference 20. As the circumference of the circle is 2π times the radius. Thus, the radius of the circle is,
[tex]20=2\pi r\\r=\dfrac{20}{\pi}[/tex]
The circle has the central angle with a 120 degree. Thus the value of length of the arc is,
[tex]s=r\times\theta\\s=\dfrac{20}{\pi}\times\dfrac{72\times\pi}{180}\\s=8\rm\; units[/tex]
Thus, the value of the length of the arc for the provided circle with circumference 20 and has an arc with a 72 degree is 8 units.
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