By applying cosine formula we got that in [tex]\triangle XYZ[/tex] if XY = 13, YZ=20, and XZ=25 then measure of angle Z to the nearest degree is 31°
What is a triangle ?
Triangle is a closed shape with 3 sides and 3 vertices.
Given that
In [tex]\triangle XYZ[/tex]
[tex]XY=13=c\\\\YZ=20=a\\\\\\XZ=25=b\\[/tex]
Now applying cosine formula in [tex]\triangle XYZ[/tex]
[tex]c^2 = b^2 + a^2 -2ba \cos C[/tex]
[tex]13^2=25^2+20^2-2\times25\times20\times\cos Z[/tex]
[tex]169=625+400-1000\times\cos Z\\\\1000\times\cos Z=1025-169\\\\\cos Z=\frac{856}{1000}\\ \\\cos Z=0.856\\\\[/tex]
Z=31.13°
measure of angle Z to the nearest degree
[tex]Z\approx[/tex] 31°
By applying cosine formula we got that in [tex]\triangle XYZ[/tex] if XY = 13, YZ=20, and XZ=25 then measure of angle Z to the nearest degree is 31°
To learn more about Triangles visit :https://brainly.com/question/23945265
