Law of Sines and Cosines

By LOS (Law of Sines), AC = 8*sqrt(3)/3.

Find AC.

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Law of cosines:

\((7\sqrt{3} )^2=9^2+x^2-2\cdot9\cdot x\cdot cos\ 150°\\ x^2-cos\ 150°\cdot18x+81-147=0\\ x=cos\ 150°\cdot 9\pm \sqrt{81\cdot cos^2\ 150°+147}\\ x=-7.79423\pm \sqrt{207.75}\\ x\in \{{\color{blue}6.6193},-22.207\}\)

\(\color{blue}\overline{AC}=6.6193\)

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