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

Question

Mathematics

Amir

2 May, 20:54

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

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Answers (1)

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Chance Hickman · Answer 1

We can use Law of Cosines to solve for the angle of Z. The solution is shown below:

cos C = (a²+b²-c²) / 2ab

cos Z = (yz² + xz² - xy²) / 2*yz*xz

cos Z = (20² + 25 - 13²) / 2*20*25

cos Z = 856 / 1000

Z=31.13°

The answer is angle 31.13°.