[tex]\displaystyle\bf\\Se~da:\\\\\Delta ABC~cu~AB=3;~BC=6~si~AC=3\sqrt{5}\\\\Se~cere:\\\\sin B = ?\\\\Rezolvare:\\\\Verificam~daca~triunghiul~este~dreptunghic.\\\\AB^2=3^2=9\\\\BC^2=6^2=36\\\\AC^2=\Big(3\sqrt{5}\Big)^2=3^3\times\Big(\sqrt{5}\Big)^2=9\times5=45\\\\Observam~ca~AC~este~latura~cea~mai~mare.\\\\AB^2+BC^2=9+36=45=AC^2\\\\\implies~\Delta ABC~este~dreptunghic~cu~ipotenuza~AC~si~cu~\sphericalangle B=90^o.\\\\\implies~\boxed{\bf sin\,B=sin\,90^o=1}[/tex]
