Rysunek z oznaczeniami długości boków oraz kątów w załączniku.
[tex]zad.1\\\\a)\\\\x^{2} =8^{2} +10^{2} \\\\x^{2} =64+100\\\\x^{2} =164~~\land~~x > 0~~\Rightarrow~~x=\sqrt{164} =\sqrt{4\cdot 41} =2\sqrt{41} \\\\Odp:~~x=2\sqrt{41}[/tex]
[tex]b)\\\\y^{2} +4^{2} =6^{2} \\\\y^{2} +16=36\\\\y^{2} =36-16\\\\y^{2} =20~~\land~~y > 0~~\Rightarrow~~y=\sqrt{20} =\sqrt{4\cdot 5}=2\sqrt{5} \\\\Odp:~~y=2\sqrt{5}[/tex]
[tex]zad.2\\\\a)\\\\sin\alpha = cos\beta =\dfrac{4}{2\sqrt{5} }= \dfrac{2}{\sqrt{5} }\cdot \dfrac{\sqrt{5} }{\sqrt{5} }=\dfrac{2\sqrt{5} }{5} \\ \\cos\alpha =sin\beta =\dfrac{2}{2\sqrt{5} } =\dfrac{1}{\sqrt{5} }\cdot \dfrac{\sqrt{5} }{\sqrt{5} }=\dfrac{\sqrt{5} }{5}\\\\tg\alpha =ctg\beta =\dfrac{4}{2} =2\\\\ctg\alpha =tg\beta =\dfrac{2}{4} =\dfrac{1}{2}[/tex]
[tex]b)\\\\sin\alpha =cos\beta =\dfrac{\sqrt{3} }{\sqrt{7} } \cdot \dfrac{\sqrt{7} }{\sqrt{7} }=\dfrac{\sqrt{21} }{7} \\\\cos\alpha =sin\beta =\dfrac{2}{\sqrt{7} } \cdot \dfrac{\sqrt{7} }{\sqrt{7} }=\dfrac{2\sqrt{7} }{7} \\\\tg\alpha =ctg\beta =\dfrac{\sqrt{3} }{2} \\\\ctg\alpha =tg\beta =\dfrac{2}{\sqrt{3} } \cdot \dfrac{\sqrt{3} }{\sqrt{3} } =\dfrac{2\sqrt{3} }{3}[/tex]
