[tex] \bf \textit{Law of Cosines}\\\\
c^2 = a^2+b^2-(2ab)cos(C)\implies
c = \sqrt{a^2+b^2-(2ab)cos(C)}
\\\\\\
\cfrac{a^2+b^2-c^2}{2ab}=cos(C)\implies cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C\\\\
------------------------------- [/tex]
[tex] \bf \begin{cases}
a=90\\
b=55\\
c=50
\end{cases}\implies cos^{-1}\left(\cfrac{b^2+c^2-a^2}{2bc}\right)=\measuredangle A
\\\\\\
cos^{-1}\left(\cfrac{55^2+50^2-90^2}{2(55)(50)}\right)=\measuredangle A\implies cos^{-1}\left(\cfrac{-2575}{5500} \right)=\measuredangle A
\\\\\\
117.91634^o\approx \measuredangle A [/tex]
