Question

Find A and please include explanation please. If you don’t know please don’t write whatever to get the points

Answer 1

$\bf \textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)cos(C)\implies c = \sqrt{a^2+b^2-(2ab)cos(C)} \\\\\\ \cfrac{a^2+b^2-c^2}{2ab}=cos(C)\implies cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C\\\\ -------------------------------$

$\bf \begin{cases} a=90\\ b=55\\ c=50 \end{cases}\implies cos^{-1}\left(\cfrac{b^2+c^2-a^2}{2bc}\right)=\measuredangle A \\\\\\ cos^{-1}\left(\cfrac{55^2+50^2-90^2}{2(55)(50)}\right)=\measuredangle A\implies cos^{-1}\left(\cfrac{-2575}{5500} \right)=\measuredangle A \\\\\\ 117.91634^o\approx \measuredangle A$