I previously asked about this, so I'll now give an example of what I was asking

The question is :-
A ship sails on a bearing of 120 degrees for 50 km, How far east has it traveled?

They book I'm using shows a typical diagram for the situation, however it then draws a right angle triangle with an acute angle of 30 degrees. Then solves the problem as cos 30= x/ 50= 43.301
I don't understand how they've done this and why

Draw an x and y axes. Then, starting at north, the y-axis, go 120 degrees to the right. That will put you at 30 degrees below the positive x axis, east. 120-90 = 30.

That is why they do that. Now to find the distance it traveled east, just use the law of cosines. 50cos(30).

But... you really don't have to do that. You can use 50sin(120) and get the same thing.