# How do you find the lengths of the arc on a circle of radius 9 feet intercepted by the central angle 60^circ?

Jul 21, 2017

Use the arc length formula (see below)!

#### Explanation:

For this particular problem (with units in mind), the formula for arc length is

$\text{Arc length } = 2 \pi r \cdot \left(\frac{x}{360} ^ \circ\right)$,

Where $x$ is the central angle measure and $r$ is the radius of the circle.

You don't really have to work too hard to remember this formula. The arc length formula is easy to remember because it is just the circumference of the circle times the central angle over ${360}^{\circ}$.

Anyway, let's continue with the problem. We are given that the central angle is ${60}^{\circ}$, and that $r$, our radius, is $9$ feet. So, let's plug that into our equation to find the arc length, in feet:

$\text{Arc length } = 2 \pi r \cdot \left(\frac{x}{360} ^ \circ\right)$

$\text{Arc length } = 2 \pi \left(9\right) \cdot \left({60}^{\circ} / {360}^{\circ}\right)$

Now, you might be tempted to plug this in your calculator, but let's simplify it a little bit more.

$\text{Arc length } = 2 \pi \left(9\right) \cdot \left({60}^{\circ} / {360}^{\circ}\right)$

$\text{Arc length } = 18 \pi \cdot \left(\frac{1}{6}\right)$

$\text{Arc length " = 3pi " feet}$

So, if you wanted an exact answer, it would be that the arc length is $3 \pi \text{ feet}$. If you wanted an approximate answer, then you can type $3$ times $\pi$ in your calculator to get a value of about $9.425 \text{ feet}$ as you alternative answer.

I hope that helps!