$\mathrm{tg}\alpha =\frac{a}{b}=1\frac{1}{3}$  

$\frac{a}{b}=1\frac{1}{3}$           $/\cdot b$

$a=1\frac{1}{3}b$

 

${\left(1\frac{1}{3}b\right)}^2+b^2={10}^2$

${\left(\frac{4}{3}b\right)}^2+b^2={10}^2$

$\frac{16}{9}{b}^2+b^2=100$

$\frac{16}{9}{b}^2+\frac{9}{9}{b}^2=100$

$\frac{25}{9}{b}^2=100$     $/:\left(\frac{25}{9}\right)$

$b^2=100\cdot \frac{9}{25}$

$b^2=\frac{900}{25}$         $/\sqrt{}$

$b=\sqrt{\frac{900}{25}}$

$b=\frac{\sqrt{900}}{\sqrt{25}}$

$b=\frac{30}{5}=\underline{\underline{6}}$

$a=1\frac{1}{3}\cdot 6=\frac{4}{\sout{3}}\cdot \sout{6}=\frac{4}{1}\cdot 2=\frac{40}{5}=\underline{\underline{8}}$

 

$\sin \beta =\frac{5}{13}=\frac{15}{c}$

$\frac{5}{13}=\frac{15}{c}$       $/\cdot c$

$\frac{5}{13}c=15$         $/:\frac{5}{13}$

$c=15\cdot \frac{13}{5}$

$c=3\cdot \frac{13}{1}$

$c=\underline{\underline{39}}$

 

${15}^2+d^2={39}^2$

$d^2=1521-225$

$d^2=1296\mid \sqrt{}$  

$d=\sqrt{36\cdot 36}$

 

$d=\underline{\underline{36}}$   

 

 

$\cos \gamma =\frac{f}{58}=\frac{20}{29}$          

$\frac{f}{58}=\frac{20}{29}$       $/\cdot 58$

$f=\frac{20}{\sout{29}}\cdot \sout{58}$

$f=20\cdot 2$

$f=40$

 

$e^2+{40}^2={58}^2$

$e^2+1600=3364$

$e^2=3364-1600$

$e^2=1764\mid \sqrt{}$

$e=\sqrt{1764}$

$e=\sqrt{42\cdot 42}$

$e=42$