[tex]ctg\alpha =\frac{cos\alpha}{sin\alpha}=\frac{8}{15}\\ \\ cos\alpha=\frac{8}{15} sin\alpha\\\\cos^2\apha+sin^2\alpha=1\\\\(\frac{8}{15} sin\alpha)^2+sin^2\alpha=1\\\\\frac{64}{225}sin^2\alpha+sin^2\alpha=1\\ \\\frac{289}{225} sin^2\alpha=1\\\\sin^2\alpha=\frac{225}{289}\\ \\sin\alpha=\sqrt{\frac{225}{289} }=\frac{15}{17}[/tex]
