Obliczam x z tw Pitagorasa:
[tex]x^{2}+9^{2}=15^{2}\\\\x^{2}+81 = 225\\\\x^{2} = 225-81 = 144\\\\x = \sqrt{144}\\\\x = 12\\\\a = 9\\b = 12\\c = 15\\\\\\sin\alpha = \frac{x}{c} =\frac{b}{c}= \frac{12}{15} = \frac{4}{5}\\\\cos\alpha = \frac{a}{c} = \frac{9}{15} = \frac{3}{5}\\\\tg\alpha = \frac{x}{a}=\frac{b}{a} = \frac{12}{9} = \frac{4}{3}[/tex]
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[tex]tg\beta = \frac{a}{x} = \frac{a}{b} = \frac{9}{12} = \frac{3}{4}\\\\sin\beta = \frac{a}{c} = \frac{9}{15} = \frac{3}{5}\\\\cos\beta = \frac{x}{c} = \frac{b}{c} = \frac{12}{15} = \frac{4}{5}[/tex]
