00:04
Okay, here's another good vector problem with a little bit of algebra to it.
00:09
We've got three islands and we know that the first two islands, the distance, is 4 .76 kilometers at an angle of 37 degrees north of east.
00:29
And so again, here's east, and so north of east is going to be that way.
00:33
And so we'll call this island one, we'll call this island two.
00:39
And then we go from those two islands.
00:42
We go to a second island, and i'm just going to put it over here.
00:49
And what we're told about that second island is we're not told its distance.
00:54
I'm just going to call the distance a, but we know that's a direction of 69 degrees west of north.
01:01
And so if north is this way, then it's one.
01:04
West of north, 69 degrees.
01:09
And finally, we come from that second island, or correction the third island, back to the first island.
01:17
And we're told that that is a direction of 28 degrees east of south.
01:26
So if this is south, this is 28 degrees.
01:29
And we don't know its distance.
01:31
So i'll just call that distance be.
01:33
And the question is asking, what is a and what is b? what are those two distances? well, before we do anything in vectors, trying to compare vectors or solve vectors, really helps, especially in this case, to convert it to component form.
01:51
And so i'm going to do that with all three of the vectors.
01:57
I'm going to get an x component and a y component.
02:01
I'm going to start with a vector from 1, to 2.
02:08
And the x component is going to be the base of this triangle.
02:14
And so that's going to be 4 .76 kilometers times the cosine because it's the adjacent times 37 degrees.
02:25
And let me get that moved over a little bit.
02:28
We're looking for that distance right there.
02:30
And that's going to be 4 .76 times the sign of 37 degrees because that's that's the the opposite and when we plug those into our calculator we get 3 .80 kilometers and 2 .86 kilometers.
02:53
The second piece is a little bit trickier.
02:58
We've got that x value.
03:00
We know that this angle here is 69 degrees and so that is the opposite and so that component, is going to be a.
03:11
We don't know what a is, and so we just use algebra.
03:14
We just write down the letter times the sign of 69 degrees.
03:20
Also note that where that vector traveled to the east, this vector travels to the west.
03:30
And so if we use north as positive and east is positive, that's going to be a negative a sign of 69 for that x component.
03:41
The y component is just going to be a it's in the positive direction times the cosine of 69 degrees and that's the distance from two to three and finally the distance from three back to one is going to be this triangle here we're looking for this x value which again is going to be sign that is b times the sign of that 28 degree angle and notice that is in the positive erection so we keep it positive the y value though is b cosine 69 degrees but that is going downward southward and so that needs to be negative b cosine times 28 and so what do we do now we have our x and y value you know we've got two a's and two b's in the equation...