00:01
Okay, so we're told that ricardo and jane start at the same point, so they're both start here.
00:06
It then says that ricardo walks 26 metres in a direction 60 degrees west of north.
00:12
Okay, so north is this way.
00:18
I'll just draw on west as well, so north, south, west, east.
00:25
And so it walks in a direction 60 degrees west of north.
00:28
So that's going to be here, where this angle is 60.
00:34
And the length is 26 meters.
00:38
It says jane walks 16 meters in a direction 30 degrees south of west.
00:44
So again this sign's going to be here, 16 meters and this will be 30 degrees.
00:51
I'll just make this one up it.
00:56
It then asks us what is the distance between them? so we're just going to basically use some trigonometry here.
01:04
So we want to find this blue length here.
01:09
Which i'll call a.
01:12
We'll call this side b and this side c, so 16 metres is c, 26 metres is b.
01:20
And we'll call the opposite angles to these sides, as it were, the corresponding capital letters.
01:29
So sorry, that should be capital a.
01:32
This should be capital c and this should be capital b.
01:37
So we can firstly see that angle a is 60 degrees, right? because the distance between b and north is 60, and then so the distance between this and this horizontal line here is going to be 30.
01:49
Added onto the 30, we know that jane walked in from west, and that makes 60 degrees.
01:56
Now, we can use the cosine rule here.
02:00
So the cosine rule says that a squared equals b squared plus c squared minus 2bc times the cosine of a.
02:09
Now we have b, b is 26, c is 16, a is 60, and so we can sub all this in to find that a is 22 .7 metres...