Question

What is the arc length?

Answer 1

do you have a picture for the question?

Answer 2

Answer:

Step-by-step explanation:

You could do this one of 2 ways.  I'll show you both ways and you decide which one works best for you to use on your own.

First, by using the circumference formula of a circle.

C = 2πr and we know the radius is 5, so the circumference of the circle is

C = 10π

1/4 of the circle is missing, so 10π/4 gives you the length of the arc that is missing.

$\frac{10\pi}{4}=2.5\pi$

10π - 2.5π = 7.5π

OR we could do the problem using the formula for the arc length which is

$AL=\frac{\theta}{360}*$2πr

The measure of the angle shown is for the missing part of the circle.  If the measure of a circle is 360, and the measure of the angle for the part of the circle that's missing is 90, then 360 - 90 is the measure of the central angle of the part of the circle that's still there.  So the measure of theta is 270°.

$AL=\frac{270}{360}*10\pi$ and simplifying a bit:

$AL=.75(10\pi)$ so the arc length is

AL = 7.5π

Use either way.  They both work.