Final answer:
The provided information about the lengths of side c in the triangle is contradictory, rendering the question unanswerable until the correct lengths are provided. The law of sines could potentially be used if the correct information were given.
Step-by-step explanation:
The student is asking whether the law of sines can be used to solve for side b in a triangle where side c is given as both 126 and 9.3, which seems to be a mistake since a triangle cannot have the same side with two different lengths. Therefore, we cannot proceed with the calculation as there is contradictory information regarding the length of side c. The law of sines is indeed a method we could use if we had a non-contradictory set of measurements, and it states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a given triangle.
To use the law of sines, one would typically need to know either two angles and one side (AAS or ASA condition) or two sides and a non-included angle (SSA condition). However, the SSA condition can sometimes result in two possible solutions, known as the ambiguous case of the law of sines, or no solution at all, depending on the relationships between the given values.