[tex]a=2\sqrt2cm\\b=2\sqrt6cm\\\\a^2+b^2=c^2\\c^2=(2\sqrt2cm)^2+(2\sqrt6cm)^2\\c^2=8cm^2+24cm^2\\c^2=32cm^2\\c=\sqrt{32}cm\\c=\sqrt{4*4*2}cm\\c=4\sqrt2cm[/tex]
[tex]sin\alpha=\frac{a}c=\frac{2\sqrt2cm}{4\sqrt2cm}=\frac12\\cos\alpha=\frac{b}c=\frac{2\sqrt6cm}{4\sqrt2cm}=\frac{\sqrt6}{2\sqrt2}=\frac{\sqrt{12}}4=\frac{2\sqrt3}4=\frac{\sqrt3}2\\tg\alpha=\frac{a}b=\frac{2\sqrt2cm}{2\sqrt6cm}=\frac{\sqrt2}{\sqrt6}=\frac{\sqrt{12}}6=\frac{2\sqrt3}{6}=\frac{\sqrt3}3\\ctg\alpha=\frac{b}a=\frac{2\sqrt6cm}{2\sqrt2cm}=\frac{\sqrt6}{\sqrt2}=\frac{\sqrt{12}}2=\frac{2\sqrt3}2=\sqrt3[/tex]
[tex]sin\beta=cos\alpha=\frac{\sqrt3}2\\cos\beta=sin\alpha=\frac12\\tg\beta=ctg\alpha=\sqrt3\\ctg\beta=tg\alpha=\frac{\sqrt3}3[/tex]
