Final answer:
In triangle AXYZ, where YZ = 11, ZX = 5, and XY = 13, the order of the angles from smallest to largest is angle Y, angle Z, and angle X.
Step-by-step explanation:
In triangle AXYZ, we know that YZ = 11, ZX = 5, and XY = 13. To determine the order of the angles, we can use the Law of Cosines. The formula is as follows:
c^2 = a^2 + b^2 - 2ab cos(C)
Using this formula, we can find the value of angle X. Substitute the known values:
169 = 25 + 121 - 2 * 5 * 11 * cos(X)
After solving the equation, we find that cos(X) = -1/13. Since cosine is negative in quadrant II, angle X is obtuse. So, the correct order of the angles from smallest to largest is angle Y, angle Z, and angle X.
Learn more about Triangle angles