00:02
Okay, so on our problem, we have one vector with a force of 4 ,000, one with a force of 5 ,000 ounce.
00:12
Okay.
00:14
So i want to draw a parallelogram, and i know the angle in between them is 50.
00:23
Well, from geometry, these two angles should add up to 180 degrees, which means this angle in here is 130 degrees, and i'm going to need that.
00:34
Because my resultant is right here.
00:38
This is my resultant.
00:40
So on a parallelogram, this side would be 4 ,000, this side would be 5 ,000.
00:46
But i really just need to use this part of my triangle.
00:49
So i'm basically going to use this triangle, 4 ,000, this side's 5 ,000.
00:56
I want my resultant, and my angle between them is 130 degrees.
01:00
So i'm going to use law of cosines, which says a square, plus b squared minus 2 a b times the cosine of the angle in between them, which in this case i'm going to call r is equal to r squared.
01:26
So i'm going to call this r.
01:28
I'm going to call this r.
01:28
I'm going to call this a.
01:30
We're going to call this b.
01:32
So my a, let me go down here, i've got 4 ,000 squared plus my 5 ,000 squared minus my 2 times my 4 ,000 times my 5 ,000, cosine of 130 degrees is equal to that resultant squared.
02:03
And if i square root this to get my resultant, and you stick all that in the calculator, you're going to get 8 ,167 .71 pounds of force.
02:17
Okay, that was part a.
02:18
Part b wanted to know what the angle was between the resultant and the 5 ,000.
02:26
So i want to figure out what this angle in here is.
02:30
So let me redraw the picture.
02:33
So now i know that i have this side is 8167 .71...