Final answer:
In triangle AXYZ, the angles can be found using the Law of Cosines. The measure of angle X is cos^(-1)(10/13), the measure of angle Y is cos^(-1)(5/11), and the measure of angle Z is 180 - X - Y.
Step-by-step explanation:
In a triangle, the angles always add up to 180 degrees. In triangle AXYZ, we know that YZ = 11, ZX = 5, and XY = 13. To find the angles, we can use the Law of Cosines.
Using the Law of Cosines, we can find the measure of angle X using the equation: cos(X) = (XY^2 + XZ^2 - YZ^2) / (2 * XY * XZ). Plugging in the values, we get: cos(X) = (13^2 + 5^2 - 11^2) / (2 * 13 * 5). Solving this, we find that cos(X) = 10/13. Taking the inverse cosine, we get X = cos^(-1)(10/13).
Similarly, we can find the measure of angle Y using the equation: cos(Y) = (YZ^2 + XY^2 - XZ^2) / (2 * YZ * XY). Plugging in the values, we get: cos(Y) = (11^2 + 13^2 - 5^2) / (2 * 11 * 13). Solving this, we find that cos(Y) = 5/11. Taking the inverse cosine, we get Y = cos^(-1)(5/11).
Finally, we can find the measure of angle Z by subtracting the sum of angles X and Y from 180 degrees. Z = 180 - X - Y.
Learn more about Triangle Angles