Look at the picture.
[tex]sine=\dfrac{opposite}{hypotenuse}\\\\\sin\angle L=\dfrac{x}{y}[/tex]
Use the Pythagorean theorem:
[tex]x^2=3^2+4^2\\\\x^2=9+16\\\\x^2=25\to x=\sqrt{25}\to x=5[/tex]
Again use the Pythagorean theorem:
[tex]y^2=5^2+12^2\\\\y^2=25+144\\\\y^2=169\to y=\sqrt{169}\to y=13[/tex]
Calculate sine:
[tex]\sin\angle L=\dfrac{5}{13}\to\boxed{B.}[/tex]
