So firstly, the hypotenuse is c for both ∠A and ∠B. That doesn't change whether you consider ∠A or ∠B.
Next, the opposite side is the side that doesn't touch the angle. In this case, ∠A's opposite side is a and ∠B's opposite side is b because the sides do not touch those angles.
Lastly, we have the adjacent side. This is the side that is, as the title says, adjacent to the angle. In this case, ∠A's adjacent side is b and ∠B's adjacent side is a because those sides are next to the angle.