00:01
A parallelogram has sides of length 16 units and 10 units.
00:05
The shorter diagonal is 12 units.
00:08
Find the measure of the longer diagonal.
00:10
Okay, before we can do that, we're gonna have to find the angle measure.
00:16
So we're gonna first find this angle.
00:19
We're just gonna call it x.
00:22
I know that using the law of cosines, i would have 12 squared equals 10 squared.
00:31
Plus 16 squared minus two times 10 times 16 times cosine x.
00:41
So let's just put numbers in for all of these squares.
00:49
This is 144, 100 plus 16 squared is i think 256, but let me say 16 squared.
01:07
Yep, 256 minus, let's see, 20, that's 320 cosine x.
01:20
Okay, so the first thing i'm gonna do is subtract 356 from both sides.
01:29
That gets rid of that.
01:32
144 minus 356 is negative 221.
01:38
And now i'm gonna divide both sides by negative 320 to get rid of this.
01:53
So i get cosine x equals, all right, negative 221 divided by negative 320 is 0 .6906.
02:17
Let me rewrite that.
02:18
0 .6906.
02:25
And i've got to get my calculator in degree mode because it was in radians...