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gmany

[tex]\text{Use the Pythagorean theorem:}\\\\AB^2+BC^2=AC^2\\\\AC^2=9^2+12^2\\\\AC^2=81+144\\\\AC^2=225\to AC=\sqrt{225}\\\\AC=15\\\\sine=\dfrac{opposite}{hypotenuse}\\\\\text{We have}\ opposite=12\ \text{and}\ hypotenuse=15.\ \text{Substitute:}\\\\\sin\alpha=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}[/tex]

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