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laila [671]
1 year ago
15

The radius of a circle is 10 miles. What is the length of a 45° arc?

Mathematics
1 answer:
pshichka [43]1 year ago
6 0

Solution

We are given

Radius (r) = 10 miles

Angle (theta) = 45 degrees

We want to find the length of the arc

Note: Formula for the length of an Arc

\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ length\text{ }Of\text{ }Arc=\frac{45}{360}\times2\times\pi\times10 \\ length\text{ }Of\text{ }Arc=\frac{1}{8}\times20\pi \\ length\text{ }Of\text{ }Arc=\frac{5}{2}\pi \\ length\text{ }Of\text{ }Arc=7.853981634 \\ length\text{ }Of\text{ }Arc=7.854miles \end{gathered}

Therefore, the length of the arc is

\begin{equation*} 7.854miles \end{equation*}

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