Final answer:
The problem given by the student is missing necessary information or contains an error which prevents solving for the measures of the remaining sides and angles of a triangle using the given values. We should clarify the problem before attempting to find a solution.
Step-by-step explanation:
The student's question involves finding the measures of the remaining sides and angles of a triangle, given certain side lengths and an angle measure. When one angle of a triangle is 111°, and the lengths of two sides are 12 and 6, we can use the Law of Sines to find the remaining angles. However, without knowing whether side 'a' is opposite angle 'A', or which side is opposite angle 'B', the problem lacks enough information to solve it directly using the data provided.
Assuming side 'a' is opposite from angle 'A' and side 'c' is opposite from angle 'C', the Law of Sines states that α / sin(A) = b / sin(B) = c / sin(C), where lowercase letters represent sides and uppercase letters represent corresponding angles. To find the measures of the remaining sides and angles, we would need to solve this equation for the unknown variables. Since the question and the information provided do not match, it's possible there is a typo or an error in the question, and it's recommended to clarify the problem before attempting to solve it.