Answer:
[tex]X=70.5^o[/tex]
Step-by-step explanation:
we know that
The formula of the law of cosines is equal to
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]
where
a, b and c are sides. C is the angle opposite side c
In this context
The formula to calculate the measure of angle X is equal to
[tex]YZ^2=XZ^2+XY^2-2(XZ)(XY)cos(X)[/tex]
substitute the given values
[tex]22^2=20^2+18^2-2(20)(18)cos(X)[/tex]
solve for cos(X)
[tex]484=400+324-(720)cos(X)[/tex]
[tex]484=724-(720)cos(X)[/tex]
[tex](720)cos(X)=724-484[/tex]
[tex](720)cos(X)=240[/tex]
[tex]cos(X)=240/720[/tex]
[tex]X=cos^{-1}(240/720)=70.5^o[/tex]
