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A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π.A. 5π/2 inchesB. 5π inchesC. 5 inchesD. 4π inches

Sagot :

[tex]5\pi\text{ inches (option B)}[/tex]

Explanation:

radius = 20 inches

angle = θ= 45°

We would apply length of an arc:

[tex]length\text{ of an arc = }\frac{\theta}{360\text{ }}\text{ }\times2\pi r[/tex][tex]\begin{gathered} \text{length of the arc = }\frac{45}{360}\times2\times\pi\times20 \\ =\text{ }\frac{1}{8}\times\text{ 40}\pi \end{gathered}[/tex]

Since the options is in terms of π, the answer will be in that form

[tex]\text{length of }arc\text{ = 5}\pi\text{ inches (option B)}[/tex]

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