00:01
Hello, we are looking at a situation where we have a circle with a central angle, and the arc length that is cut out is four units, and the area of the sector cut out is 32 square units, and we want to know what the radius is, and we want to know what theta is.
00:20
So there's a couple of things we need to know.
00:23
First of all, arc length is the fraction of the total number of radians all the way around, and so if we were to look at comparing our angle theta to 2 pi, because there's 2 pi radiance in a circle, and multiply by circumference, which is 2 pi r, one of the things we notice is that you actually get a nice simple formula, theta times r, is equal to your arc length.
00:51
So one thing that we know is that theta r equals 4, because the arc length is 4.
00:58
The other thing we need to do is look at the fraction of the circle times pi r squared because we want to know about the area.
01:09
And in this case, the pies will cancel.
01:11
So we'll get something like theta over two times r squared.
01:16
All right.
01:17
And we happen to know that theta over two times r squared is equal to 32.
01:24
And that actually gives us a system of equations that we can solve.
01:27
So let's go ahead and solve that system of equations...