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The arc corresponding to a central angle of 125 degrees in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places.

Sagot :

[tex] \frac{Angle}{360} [/tex] x [tex]2 \pi r[/tex]

[tex] \frac{125}{360} [/tex] x [tex]2 \pi (10)[/tex] = [tex]21.82[/tex]

Answer: The Arc measures [tex]21.82 feet[/tex]
Calculistaidn

Answer:

[tex]21.82\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a complete circle is equal to

[tex]C=2\pi r[/tex]

In this problem we have

[tex]r=10\ ft[/tex]

substitute

[tex]C=2\pi (10)=20 \pi\ ft[/tex]

Remember that

An angle of [tex]360\°[/tex] subtends the arc length of a complete circle

so

by proportion

Find the arc length for an angle of [tex]125\°[/tex]

[tex]\frac{20 \pi}{360}\frac{feet}{degrees}=\frac{x}{125}\frac{feet}{degrees}\\ \\x=125*(20\pi )/360\\ \\x=21.82\ ft[/tex]

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