Answer :
The sine function is defined as:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex]For angle C the opposite leg is the segment AB and the hypotenuse is AC, then we have that:
[tex]\sin C=\frac{AB}{AC}[/tex]Now since the triangles are similar that means that the sine of F should be equal to the sine of C. In this case the opposite leg is DE and the hypotenuse is DF, then:
[tex]\sin C=\sin F=\frac{DE}{DF}[/tex]Therefore the ratios that are equal to sin C are options A and D.