Bonjour Supersong
Par le théorème d'al Kashi,
[tex]AC^2=AB^2+BC^2-2\times AB\times BC\times\cos(\widehat{ABC})[/tex]
[tex](\sqrt{34})^2=6^2+(\sqrt{34})^2-2\times 6\times \sqrt{34}\times\cos(\widehat{ABC})[/tex]
[tex]34=36+34-12\times \sqrt{34}\times\cos(\widehat{ABC})[/tex]
[tex]12\sqrt{34}\times\cos(\widehat{ABC})=36+34-34[/tex]
[tex]12\sqrt{34}\times\cos(\widehat{ABC})=36[/tex]
[tex]\cos(\widehat{ABC})=\dfrac{36}{12\sqrt{34}}[/tex]
[tex]\cos(\widehat{ABC})=\dfrac{3}{\sqrt{34}}[/tex]
[tex]\widehat{ABC}=\cos^{-1}(\dfrac{3}{\sqrt{34}})[/tex]
[tex]\boxed{\widehat{ABC}\approx59^o}[/tex]
