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A circular arc has measure of 4 cm and is intercepted by a central angle of 73°. Find the radius r of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.r= __ cm

Sagot :

The arc lenghr is given by:

[tex]s=r\theta[/tex]

where s is the arc lenght, r is tha raidus and theta is the angle measure in radians. Since in our problem the angle is given in degrees we have to convert it to radians, to do this we have to multiply the angle by the factor:

[tex]\frac{\pi}{180}[/tex]

Then:

[tex]\theta=(73)(\frac{\pi}{180})[/tex]

Plugging the value of the arc lenght and the angle in the first formula, and solving for r we have:

[tex]\begin{gathered} 4=r(73)(\frac{\pi}{180}) \\ r=\frac{4\cdot180}{73\cdot\pi} \\ r=3.1 \end{gathered}[/tex]

Therefore, the radius of the circle is 3.1 cm.

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