Answer:
Choice D.
82.8
Step-by-step explanation:
We can use law of cosines since we are given three sides.
[tex]z^2=y^2+x^2-2yx \cos(Z)[/tex]
Since [tex]z[/tex] is opposite side of angle [tex]Z[/tex], then [tex]z=12[/tex]:
[tex]12^2=10^2+8^2-2(10)(8) \cos(Z)[/tex]
[tex]144=100+64-160 \cos(Z)[/tex]
[tex]144=164-160 \cos(Z)[/tex]
[tex]-20=-160 \cos(Z)[/tex]
[tex]\frac{-20}{-160}=\cos(Z)[/tex]
[tex]\frac{20}{160}=\cos(Z)[/tex]
[tex]\frac{1}{8}=\cos(Z)[/tex]
[tex]\cos^{-1}(\frac{1}{8})=Z[/tex]
[tex]82.819^\circ=Z[/tex]
Option D is correct.
