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In ΔDEF, \( d = 190 \, \text{cm} \), \( e = 580 \, \text{cm} \), and \( f = 730 \, \text{cm} \).

Find the measure of \(\angle D\) to the nearest degree.

Answer :

Check the picture below.

[tex]\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{580^2+730^2-190^2}{2(580)(730)}\right)=\measuredangle D \implies \cos^{-1}\left(\cfrac{ 833200 }{ 846800 }\right)=\measuredangle D \\\\\\ \cos^{-1}(0.9839395) \approx \measuredangle D \implies 10^o \approx \measuredangle D[/tex]

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