Question

Can someone please explan how I got this wrong?

Answer 1

$\bf \textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)cos(C)\implies c = \sqrt{a^2+b^2-(2ab)cos(C)} \\\\\\ \cfrac{a^2+b^2-c^2}{2ab}=cos(C)\implies cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C\\\\ -------------------------------\\\\ \begin{cases} x=24\\ a=25\\ b=19 \end{cases}\implies cos^{-1}\left(\cfrac{25^2+19^2-24^2}{2(25)(19)}\right)=\measuredangle x \\\\\\ cos^{-1}\left( \cfrac{41}{95} \right)=\measuredangle x\implies 64.432194^o\approx \measuredangle x$