In triangle ΔXYZ, XY = 13, YZ = 20, and XZ = 25. What is the measure of angle Z to the nearest degree?

Question

A. 59°
B. 62°
C. 31°
D. 74°

Answer 1

Using the law of cosines, we can find cos(Z):

cos(Z) = (XY² + XZ² - YZ²)/(2XY*XZ)
cos(Z) = (13² + 25² - 20²)/(2*13*25)
cos(Z) = 0.64

Taking the inverse cosine, we get:
Z ≈ 50.7°

To the nearest degree, Z ≈ 51°, which is closest to answer choice A. Therefore, the correct answer is A. 59°.