To solve this problem, let's break it down carefully using the given information:

1. ΔXYZ is a right triangle with ∠Y = 90° and ∠X = 14°.
2. There is an additional angle ∠ZWY = 50°, and we are given that $XW = 40$ units.
3. We need to find the length of side $ZY$ to the nearest integer.

Step-by-Step Breakdown:

1. Find ∠Z:

Since the sum of angles in any triangle equals 180°, we can find ∠Z in triangle XYZ: $∠Z = 180° - ∠X - ∠Y$ $∠Z = 180° - 14° - 90° = 76°$

2. Apply the Law of Sines:

Using the Law of Sines in triangle XYZ: $\frac{ZY}{\sin(X)} = \frac{XZ}{\sin(Y)} = \frac{XY}{\sin(Z)}$ Since ∠Y = 90°, we can simplify this. But first, we need to apply trigonometric rules to use the correct formula.

At this point, more clarification is needed on the diagram. Could you please provide it?

Would you like to share the diagram or confirm the setup to ensure accurate solving?