Final answer:
The given values in the triangle XYZ do not allow the direct use of Law of Cosines to find length of side y; additional information or clarification of angle values is needed to proceed with the calculation.
Step-by-step explanation:
To find the length of side y in triangle XYZ, where side z is 92 inches, side x is 44 inches, and angle ∠y is 49°, we can use the Law of Cosines. The Law of Cosines states that c² = a² + b² - 2ab*cos(∠C), where c is the side opposite to angle C, and sides a and b are the other two sides of the triangle. Since we do not have ∠y opposite to any known side, we first need to find ∠x or ∠z using the Law of Sines (a/sin(∠A) = b/sin(∠B) = c/sin(∠C)). Once we have either of these angles, we can use the Law of Cosines to find the length of side y. Since the information given does not allow for a direct calculation, we cannot provide a definitive answer. The student may need to verify the given values or provide additional information.