List the angle measures of △UVW in order from smallest to largest, given that VW=73 meters, UW=59 meters, and UV=40 meters.

To solve this problem, we will use the law of cosines. The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ opposite side c, the following equation holds true:

c² = a² + b² - 2ab cos(γ)

We can use this law to find each angle of the triangle.

1. First, let's find angle V (opposite side UV). We'll plug the given side lengths into the law of cosines:

40² = 59² + 73² - 25973*cos(V)

Solving for cos(V), we get:

cos(V) = (59² + 73² - 40²) / (25973)

Then, we find the angle V by taking the arccos of cos(V).

2. Next, we'll find angle U (opposite side UW). Again, we'll use the law of cosines:

59² = 40² + 73² - 24073*cos(U)

Solving for cos(U), we get:

cos(U) = (40² + 73² - 59²) / (24073)

Then, we find the angle U by taking the arccos of cos(U).

3. Finally, we'll find angle W (opposite side VW). We can find this angle by subtracting the other two angles from 180°, since the sum of the angles in a triangle is always 180°:

W = 180° - V - U

After finding the three angles, we can list them in order from smallest to largest.