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Find C round to the nearest tenth.

Find C round to the nearest tenth.-example-1
User Alizelzele
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2 Answers

5 votes

Answer:

C=29.4°

Explanation:


c=50\:ft\\\\a=90\:ft\\\\b=55\:ft

Using law of Cosines


C=cos^(-1)\left(\cfrac{a^2+b^2-c^2}{2ab}\right)\\\\C=cos^(-1)\left(\cfrac{90^2+55^2-50^2}{2*90*55\right)}\\\\C=29.4^(o)

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User Michael Salmon
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3.8k points
8 votes


\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] \rule{34em}{0.25pt}\\\\ cos^(-1)\left(\cfrac{90^2+55^2-50^2}{2(90)(55)}\right)=\measuredangle C\implies cos^(-1)\left( \cfrac{8625}{9900} \right)=\measuredangle C \\\\\\ cos^(-1)\left( \cfrac{115}{132} \right)=\measuredangle C\implies 29.4^o\approx \measuredangle C

User Laurence Fass
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