00:01
In your question, we have this pontoon boat, which i'm going to start right here.
00:04
I'm going to put in a south line, and we're told that it's traveling on a bearing of south 65 degrees to the west.
00:14
So 65 degrees, i'm going to go ahead and just approximate that.
00:19
This is 65 degrees.
00:24
Now, we know that that was occurring at 25 miles per hour, so i'll just put a 25 there for that.
00:31
It hits a current that is traveling at 6 miles per hour in the north 15 degrees west direction.
00:41
So i'm going to go ahead and draw in a north line from this position.
00:52
And we have 15 degrees to the west, which would be this direction.
00:56
Here, we'll say that's 15 degrees.
01:01
And this number is a 6 for the speed.
01:07
We're to find the resultant magnitude and direction of the boat.
01:12
So here was the starting point.
01:15
What we're trying to do is to get the magnitude of that direction and the angle of that direction.
01:28
Okay, so let's start with trying to determine some angles here.
01:33
We know this angle right here would be 65 degrees because the north and south lines would be parallel, giving us an alternate interior angle relationship.
01:51
That makes this angle right here total 80 degrees, that whole angle.
01:58
So what i want to kind of do here is draw that triangle separately, and i'll put the 80 right here.
02:10
We have 6 and 25.
02:13
Let me label this abc, and what we can use is the law of cosines to find the missing side lowercase b...