Question

In ΔDEF, d = 190 cm, e = 580 cm and f=730 cm. Find the measure of ∠D 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{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`

Make sure your calculator is in Degree mode.