Question

In △ABC

, a=31
, b=22
, and c=18
. Identify m∠A
rounded to the nearest degree.

Answer 1

Check the picture below.

`\textit{Law of Cosines}\\\\ \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 \\\\[-0.35em] ~\dotfill\\\\ \cos^(-1)\left(\cfrac{22^2+18^2-31^2}{2(22)(18)}\right)=\measuredangle A \implies \cos^(-1)\left(\cfrac{ -153 }{ 792}\right)=\measuredangle A \\\\\\ \cos^(-1)\left(\cfrac{ -17 }{ 88}\right)=\measuredangle A\implies 101^o\approx \measuredangle A`

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