a boy walks 1260m on a bearing of 120°.How far south is he from his starting point?

I assume you mean he walks on a heading of 120.

You travel on a heading.
You take a bearing on something else, maybe a lighthouse or a ship.
Anyway in the x, y coordinates that your math text should have stuck to:
120 clockwise from north is 30 degrees below the positive x axis.
so the -y, or south, distance is 1260 sin 30
luckily sin30 is 1/2
so
1260 / 2 meters South