Question

Solve the problem.

A pendulum swinging through a central angle of 108° completes an arc of length 24 cm. What is the length of the
pendulum? Round to the nearest hundredth.

Answer 1

Yes! I was looking to refresh my geometry skill!

Explanation:

So, a 108* arc is 24 cm. How to solve it?

First, we need to find the Circumference, or perimeter of the circle. (That the swinging pendulum makes.

Second, use that in the formula for circumference, and find the radius.

Third, done! So, let's get to it!

All we have to do to find the circumference is divide 24 by 108, then multiply that by 360*(because a circle is 360*).

`24/108*360=80`

So, our circumference is 80cm. Nice! Just need to input that into the circumference formula.

`80=2\pi *r\\`

Now, to solve...

`40=\pi *r\\40/\pi =r`

This rounds to about 12.73 cm.

Hope this helps!

Happy Geometry!