00:01
We have a picture in which the navigator of an airplane plans a flight from one airport to another.
00:05
So we're going to go from here to here.
00:07
And i have these actually as velocity vectors now, not as distances, but we'll change them into distances momentarily.
00:14
And so we know that it's in one direction that is north, 30 degrees east.
00:19
So this is the location at the airport, and this is where the pilot needs to go.
00:25
And so the pilot wants to maintain an airspeed of 400 kilometers per hour, and there is a prevailing wind from the west.
00:32
So here in red is the westerly wind, and then the plane needs to have this result in the vector so that it is moving in this direction.
00:42
So we need to find what this.
00:45
We're going to find what this angle is eventually, but we are going to have to find this angle.
00:53
So we know that the sign of theta is to the sign, oh, excuse me.
00:59
The sign of theta is to the side opposite, which is 75, as the sign of 60 degrees is to that 400.
01:14
And we know that this is an obtuse, or excuse me, an acute angle.
01:17
So we want to make sure our calculators in degree mode.
01:20
And let me grab my calculator.
01:23
So making sure my calculator is in degree mode, it is.
01:26
We have 75 times the sign of 60 degrees, which we already know is square root of 3 over.
01:32
2 divided by 400 and then we're going to inverse sign that value to get that angle and that angle of theta is that 9 .345 degrees so that's this angle so now we can add 60 degrees to that and then take 180 degrees minus that 69 .345 .5.
02:03
And that will give us this angle...