Question

55
Solve for C.
Measure of Angle C
90
C = [?]°
Round your final answer
to the nearest tenth.
с
50
Law of Cosines: c² = a² + b² - 2ab.cosC
→

Answer 1

$\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{50^2+90^2-55^2}{2(50)(90)}\right)=\measuredangle C \implies \cos^{-1}\left(\cfrac{ 7575 }{ 9000 }\right)=\measuredangle C \\\\\\ \cos^{-1}(0.8416667) \approx \measuredangle C \implies 32.7^o \approx \measuredangle C$

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