Answer
Given a, A, and C in triangle ABC, the values of side c, angle B, and side b have one possible value each. Therefore, the possibility of the ambiguous case does not exist.
Work Step by Step
If we are given a, A, and C in triangle ABC, then we can use the law of sines to find side c. Since the value of side c has one possible value, this case is not ambiguous.
Angle B also has one possible value since $A+B+C = 180^{\circ}$. Then we can use the law of sines to find side b. Since the value of side b has one possible value, this case is not ambiguous.
