To find the measure of angle X, we can use the Law of Cosines.
Let's denote angle X as θ.
Using the Law of Cosines, we have:
YZ^2 = XY^2 + XZ^2 - 2 * XY * XZ * cos(θ)
Plugging in the values given:
8^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(θ)
64 = 81 + 36 - 108cos(θ)
64 = 117 - 108cos(θ)
108cos(θ) = 117 - 64
108cos(θ) = 53
cos(θ) = 53/108
θ ≈ cos^(-1)(53/108) ≈ 55.9 degrees
Therefore, the measure of angle X to the nearest degree is approximately 56 degrees.
In triangle XYZ, XY = 9 feet, XZ = 6 feet, and YZ = 8 feet. What is the measure of angle X to the nearest degree?
1 answer