[tex]\frac{a}{sin\alpha}=\frac{b}{sin\beta}=\frac{c}{sin\gamma}\\\\c=\sqrt2\\b=\sqrt{37}\\\beta=135\\\\\frac{b}{sin\beta}=\frac{c}{sin\gamma}=\frac{a}{sin\alpha}\\\frac{\sqrt{37}}{sin135}=\frac{\sqrt2}{sin\gamma}\\\frac{\sqrt{37}}{sin(90+45)}=\frac{\sqrt2}{sin\gamma}\\\frac{\sqrt{37}}{cos45}=\frac{\sqrt2}{sin\gamma}\\[/tex]
[tex]\frac{\sqrt{37}}{\frac{\sqrt2}2}=\frac{\sqrt2}{sin\gamma}\\\sqrt{37}sin\gamma=\frac{\sqrt2}2*\sqrt2\\\sqrt{37}sin\gamma=\frac22\\\sqrt{37}sin\gamma=1 /:\sqrt{37}\\sin\gamma=\frac{1}{\sqrt{37}}\\sin\gamma=\frac{\sqrt{37}}{37}=0.16439898..\\\gamma=9\\\alpha=180-(135+9)=180-144=36\\\\[/tex]
[tex]\frac{a}{sin36}=\frac{b}{cos45}\\\frac{a}{0.5878}=\frac{\sqrt{37}}{\frac{\sqrt2}2}\\\frac{\sqrt2}2a=\sqrt{37}*0.5857 /*\frac2{\sqrt2}\\a=\frac{2\sqrt{37}}{\sqrt2}*0.5857\\a=\sqrt{74}*0.5857\\a=5.04[/tex]
