In ΔWXY, y = 940 inches, mm∠Y=100° and mm∠W=38°. Find the length of w, to the nearest inch.

To solve this problem, we will 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.

First, let's find the measure of ∠X. We know that the sum of the angles in a triangle is 180°. So, ∠X = 180° - ∠Y - ∠W = 180° - 100° - 38° = 42°.

Now, we can use the Law of Sines to find the length of side w. We have:

w/sin(∠W) = y/sin(∠Y)

Substituting the given values, we get:

w/sin(38°) = 940 inches/sin(100°)

Solving for w, we get:

w = (940 inches * sin(38°)) / sin(100°)

Using a calculator to find the sine values and perform the multiplication and division, we find that w is approximately 588 inches, to the nearest inch.