Final answer:
The length of AC can be found using the formula AC = AB + BC. Since the information provided only allows us to approximate the length of the arcs A'B' and C'B' in the larger circle, we cannot determine the exact length of AC.
Step-by-step explanation:
The length of AC can be found using the formula AC = AB + BC. Since the triangle AA'B'C' is a rotation of triangle AABC by 180 degrees, we can see that AB is equal in length to A'B' and BC is equal in length to C'B'. Therefore, AC = AB + BC = A'B' + C'B'.
Using the information given, we can approximate the length of A'B' and C'B' as the length of the corresponding arcs in the larger circle. Since the angle of rotation is 180 degrees, the arc length is half the circumference of the circle. Let's say the radius of the circle is r units. The circumference of the circle is 2πr units. So, the length of A'B' and C'B' is approximately πr units each.
Therefore, the length of AC is A'B' + C'B' = πr + πr = 2πr units. Since the radius r is not given, we cannot determine the exact length of AC. So the answer cannot be determined from the given information.