Answer:
[tex]X=68\°[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines to the triangle of the figure
[tex]yz^2=xy^2+xz^2-2(xy)(xz)cos(X)[/tex]
substitute the given values
[tex]9^2=8^2+8^2-2(8)(8)cos(X)[/tex]
Solve for X
[tex]81=64+64-128cos(X)[/tex]
[tex]81=128-128cos(X)[/tex]
[tex]128cos(X)=128-81[/tex]
[tex]128cos(X)=47[/tex]
[tex]cos(X)=\frac{47}{128}[/tex]
using a calculator
[tex]X=cos^{-1}(\frac{47}{128})[/tex]
[tex]X=68\°[/tex]
