well, you can look at it this way, if you bend down and put your eye on the angle, the side that you will see across the triangle is going to be the opposite side, so the opposite side is always the side facing off the angle. The adjacent side, is the "adjacent" or "next to" the angle, well, the opposite is across the expanse so is not touching the angle, so the other side that's not slanted is the adjacent or next to the angle.
In this case if we put our eye on the vertex A, what's across the expanse is BC, so the adjacent must be AB.
