00:01
So in these two problems, what you're being asked to do is to find the length of s and the area.
00:05
Well, s in this particular problem represents the arc lane for both of these intercepted arcs here.
00:12
And the area represents the area for the sector.
00:16
Well, let's start with number 87.
00:18
Well, we have a formula to help us find the arc length, which is s.
00:21
S is equal to the radius times theta, the measure of the central angle, as long as it turns to radiance.
00:27
Well, in our case, it is because we have pi over three radiance.
00:30
So we just have to substitute in 2 for r and pi over 3 in place of theta.
00:35
So we have s equal to 2 times pi over 3.
00:39
So now to find our arc length, we simply just need to go to our calculator.
00:43
Well, 2 times pi divided by 3.
00:46
In this case, it looks like they want us to round three places after the decimal.
00:49
So the arc length in this case would be approximately 2 .094 feet.
00:55
So now we've found the arc length.
00:56
Now we just have to go and find the area of the sector.
00:59
Well, we have a formula to do this.
01:00
It's a equals 1 half r squared theta.
01:04
And again, theta has been in terms of radiance, which ours is.
01:07
So we're going to substitute in 2 in place of r, and pi over 3 in place of theta.
01:13
So first, we have 2 squared, which is 4.
01:15
So then we have half of 4, which is 2.
01:17
So a would equal to 2 times pi over 3.
01:20
Well, that's the same as it happened to be before...