00:05
All right.
00:06
So we're being told that we have an angle measure whose terminal side is intersecting a circle at the coordinate to two radical three.
00:30
And what we're looking for is the length of the arc being intercepted by that angle.
00:39
So we have an arc length formula that says s is equal to r times theta, the radius times the measure of the angle.
00:50
I have neither of those pieces of information right now.
00:55
So we have a little bit of work that we have to do.
00:59
Right now, if we recognize that to get to the coordinate 2, 2 radical 3, i had to go to the right 2, and i had to go up to radical 3.
01:13
So what we have here is the right triangle.
01:16
And using the pythagorean theorem, 2 squared plus 2 radical 3 squared has to equal r squared.
01:26
So it's going to be 4 plus 2 radical 3 squared.
01:29
It's going to be 4 times 3.
01:30
That's going to be 12.
01:33
16 is r squared.
01:37
So now i know the radius is 4...