What is the arc length?

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.

10π - 2.5π = 7.5π

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

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°.

and simplifying a bit:

so the arc length is

AL = 7.5π

Use either way.  They both work.

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