In ΔXYZ, z = 92 inches, x = 44 inches and ∠Y=49°. Find the length of y, to the nearest inch.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Here's how you can apply it:

1. First, find the measure of ∠Z. Since the sum of the angles in a triangle is 180°, you can subtract the given angles from 180° to find ∠Z. So, ∠Z = 180° - 49° - ∠X. But we don't know ∠X yet.

2. To find ∠X, we can use the Law of Sines. According to the Law of Sines, (z/sin∠Z) = (x/sin∠X). We know that z = 92 inches and x = 44 inches. We can plug these values into the equation and solve for sin∠X.

3. sin∠X = (x * sin∠Z) / z = (44 * sin∠Z) / 92.

4. Once we find sin∠X, we can find the measure of ∠X using the inverse sine function.

5. After finding ∠X, we can find ∠Z using the equation from step 1.

6. Finally, we can find y using the Law of Sines again. According to the Law of Sines, (y/sin∠Y) = (z/sin∠Z). We know that sin∠Y = 49° and we have found ∠Z in the previous step. We can plug these values into the equation and solve for y.

7. y = (z * sin∠Y) / sin∠Z = (92 * sin49°) / sin∠Z.

8. Round your answer to the nearest inch.

Please note that this solution assumes that the triangle is not a right triangle. If it is a right triangle, you would use the Pythagorean theorem instead of the Law of Sines.