In ΔWXY, w = 470 inches, mm∠W=55° and mm∠X=42°. Find the length of y, to the nearest 10th of an inch.

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

Here's how you can apply it:

1. First, find the measure of angle Y. Since the sum of the angles in a triangle is 180°, you can subtract the measures of angle W and angle X from 180°.

   ∠Y = 180° - 55° - 42° = 83°

2. Now, you can use the Law of Sines to find the length of side y. Set up the equation like this:

   w/sin(W) = y/sin(Y)

3. Substitute the given values into the equation:

   470/sin(55°) = y/sin(83°)

4. Solve the equation for y:

   y = (470 * sin(83°)) / sin(55°)

5. Calculate the value of y to find the length of side y to the nearest tenth of an inch.

Remember to use your calculator's degree mode for the trigonometric calculations.