Question

Triangle ABC has side lengths a=79.1, b= 54.3, and c= 48.6. What is the measure of angle A ?

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{54.3^2+48.6^2-79.1^2}{2(54.3)(48.6)}\right)=\measuredangle A \\\\\\ \cos^(-1)\left(\cfrac{ -946.36 }{ 5277.96}\right)=\measuredangle A\implies 100.33^o\approx \measuredangle A`

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