Question

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

Answer 1

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

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