Question

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

Answer 1

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=(\theta)/(360)*2\pi r \\ length\text{ }Of\text{ }Arc=(45)/(360)*2*\pi*10 \\ length\text{ }Of\text{ }Arc=(1)/(8)*20\pi \\ length\text{ }Of\text{ }Arc=(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*}`