a-bok,podstawa sześcianu
b-linia płaszczyzny
[tex]6a^{2} =150\\a^{2} =25\\a=5[/tex]
[tex]cos\alpha =\frac{1}{3} \\sin^{2} \alpha +cos^{2}\alpha =1\\sin\alpha =\sqrt{1-cos^{2}\alpha } \\sin\alpha =\frac{2\sqrt{2} }{3} \\\frac{a}{b} =sin\alpha \\\frac{5}{b} =\frac{2\sqrt{2} }{3} \\b=\frac{15\sqrt{2} }{4} \\P=a*b=\frac{75\sqrt{2} }{4}[/tex]
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a-bok,podstawa sześcianu
b-linia płaszczyzny
[tex]6a^{2} =150\\a^{2} =25\\a=5[/tex]
[tex]cos\alpha =\frac{1}{3} \\sin^{2} \alpha +cos^{2}\alpha =1\\sin\alpha =\sqrt{1-cos^{2}\alpha } \\sin\alpha =\frac{2\sqrt{2} }{3} \\\frac{a}{b} =sin\alpha \\\frac{5}{b} =\frac{2\sqrt{2} }{3} \\b=\frac{15\sqrt{2} }{4} \\P=a*b=\frac{75\sqrt{2} }{4}[/tex]