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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In a circle whose radius has length 12 m, the length of an arc is 6 π m. What is the degree measure of that arc?

To determine

To find:

The degree measure of an arc.

Explanation

Formula:

Length of an arc:

In a circle whose circumference is C, the length l of an arc whose degree measure is m is given by:

l=m360×C

We know that, circumference of a circle is given by 2πr where r is the radius of circle.

Hence, length l of an arc =m360×2πr

Calculation:

The radius of circle is given as 12 m. Thus, r=12 m

The length of arc is given as 6π m.

We know that, if m is the degree measure of an arc in a circle of radius r, then length of the arc is given by the formula:

Length of arc =m360×2πr

Let’s substitute the values of r and length of arc to find the value of m

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