[tex]Zadanie\\\\c=50\ cm\\tg\alpha=\frac{3}{4}\\a,\ b\ -\ przyprostokatne\\\\tg\alpha= \frac{3}{4}=\frac{a}{b}\\\\4a=3b\ \ \mid:4\\\\a=\frac{3}{4}b\\\\a^{2}+b^{2}=c^{2}\\\\ (\frac{3}{4}b)^2+b^2=50^2\\\\\frac{9}{16}b^2+b^2=2500\\\\\frac{25}{16}b^2= 2500\ \ \mid\cdot\frac{16}{25}\\\\b^2=1600\\\\b=\sqrt{1600}\\\\b=40\ m\\\\ a= \frac{3}{4}b=\frac{3}{4}\cdot40=30\ m\\\\P=\frac{1}{2}\cdot a\cdot b\\\\P=\frac{1}{2} \cdot30\cdot40=15\cdot40=600\ m^2[/tex]
