To find angle C using the Law of Sines, the equation sinC/45 = sin135/92.5 is set up. To solve for sinC, isolate it by multiplying both sides by 45, resulting in sinC = (45/92.5) * sin(135). After performing the calculation, the angle C is determined to be approximately 20.1°. The discussion also notes that this problem relates to a physics question involving acceleration and direction change. Understanding the algebra and applying arcsin is crucial for reaching the correct answer.