Final answer:
To find the measure of angle Y in triangle XYZ, we can use the Law of Cosines.
Step-by-step explanation:
To find the measure of angle Y in triangle XYZ, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2ab*cos(C).
In triangle XYZ, we have XY = 6.32, YZ = 5.83, and XZ = 11.05. We want to find the measure of angle Y, which is opposite side YZ. Plugging in the values into the Law of Cosines, we get: (5.83)^2 = (6.32)^2 + (11.05)^2 - 2 * 6.32 * 11.05 * cos(Y).
Simplifying the equation and solving for cos(Y), we find cos(Y) = 0.3008. Taking the inverse cosine of 0.3008 using a calculator, we get Y ≈ 72.26 degrees.