Mathematics
Dollahite886
42

What is the arc length of the subtending arc for an angle of 72 degrees on a circle of radius 4?

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(1) Answers
jackie1977

Let [latex]L[/latex] be the length of an arc subtended by an angle of [latex]\theta[/latex] on a circle of radius [latex]r[/latex]. Then the ratio of the arc's length to its subtended angle is proportional with the circle's entire circumference to one complete revolution: [latex]\dfrac{2\pi r}{2\pi}=\dfrac{L}{\theta}[/latex] Solving for [latex]L[/latex] yields the formula for arc length of a circular arc, [latex]L=r\theta[/latex] where [latex]\theta[/latex] is in radians. To convert to degrees, use the conversion factor [latex]\dfrac{180^\circ}{\pi\text{ rad}}[/latex]. [latex]L=4\times\left(72^\circ\times\dfrac{\pi\text{ rad}}{180^\circ}\right)=4\times\dfrac{2\pi}5=\dfrac{8\pi}5\approx5.0265[/latex]

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