Explanation:
imagine the triangle being flipped upwards around DE, so that F is on top instead of on the bottom.
then you see clearly that
DF (21) is the radius of the trigonometric circle,
DE is cos(angle D)×radius,
EF (8) is sin(angle D)×radius.
so,
8 = sin(angle D)×21
sin(angle D) = 8/21 = 0.380952381...
angle D = 22.39268781...° ≈ 22.4°
and so, something is wrong with your problem definition.
the answer options seem to aim for angle F, for which EF (8) is the cosine × radius.
but for angle D EF is clearly the sine × radius.
and for answer option b (20.9°) EF would have to be about 7.5 units long (with the radius DF still being 21). that is all too much off.
your teacher made a mistake. send him/ her my regards.