Final answer:
The angles of triangle ABC can be found using the Law of Cosines. Given the lengths of AB, AC, and BC, the value of angle C can be determined by solving a cosine equation. However, we cannot determine the individual values of angles A and B with the given information.
Step-by-step explanation:
The angles of triangle ABC can be found using the Law of Cosines. First, let's label the angles of the triangle as A, B, and C. We can use the Law of Cosines formula: c^2 = a^2 + b^2 - 2ab * cos(C), where a, b, and c are the lengths of the sides opposite to angles A, B, and C, respectively.
Given AB = 9, AC = 11, and BC = 10, we can substitute the values into the formula:
10^2 = 9^2 + 11^2 - 2 * 9 * 11 * cos(C)
Simplifying, we have:
100 = 81 + 121 - 198 * cos(C)
Combining like terms:
-102 = -198 * cos(C)
Dividing both sides by -198:
cos(C) = -102/-198 = 0.5151
Taking the inverse cosine, we find:
C = cos^(-1)(0.5151) = 59.69 degrees
Now that we have the value of angle C, we can find angles A and B by using the fact that the sum of the angles in a triangle is 180 degrees. Since we know the value of angle C, we can subtract it from 180 to get the sum of angles A and B:
A + B = 180 - C
Substituting the values:
A + B = 180 - 59.69
A + B = 120.31
Since we don't have enough information to determine the individual values of angles A and B, we cannot sort them in order from smallest to largest.