So this is one special case where ambiguous results might happen?

Potential ambiguity arises when the sine of an angle is used to determine the angle, but it's usually easy to determine the correct value. Some textbooks don't cover this in detail.

In the example originally posted, the cosine method needs to be applied first, as no angle is known initially. Having found that angle A, say, is arccos(203/220), which is approximately 22.672 degrees, one can choose to find sin(B), which turns out to be 0.8479976415..., and arcsin of that is 57.994545... degrees. If angle B had that value, angle C would be obtuse, which is impossible, as AB isn't the longest side of the triangle (if a triangle has an obtuse angle, the side opposite that angle must be longer than each of the other two sides, because the obtuse angle must be greater than each of the other two angles). Hence angle B = 180° - 57.994545... degrees = 122.00545... degrees. If that explanation is considered too cumbersome, one can use the cosine method instead to show that cos(B) = -0.53 exactly, etc.