Answer:
4/5
Step-by-step explanation:
Look at the picture.
[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]
We need a hypotenuse length.
Use Pythagorean theorem:
[tex]hypotenuse^2=leg^2+leg^2[/tex]
We have
[tex]leg=9,\ leg=12,\ hypotenuse=x[/tex]
Substitute:
[tex]x^2=9^2+12^2\\\\x^2=81+144\\\\x^2=225\to x=\sqrt{225}\\\\x=15[/tex]
For the sine we have:
[tex]opposite=12, hypotenuse=15[/tex]
Substitute:
[tex]\sin\alpha=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}[/tex]
