Answer:
C. cos E
Step-by-step explanation:
We have been given a right triangle DEF. We are asked to find the trigonometric ratio, which has the same value as sin D.
We know that measure of angle F is 90 degrees as all angles of triangle add up-to 180 degrees. The side DE is hypotenuse of triangle DEF.
Let us find sin D for our given triangle.
[tex]\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{Sin(D)}=\frac{\text{FE}}{\text{DE}}[/tex]
We know that cosine relates adjacent side of right triangle to hypotenuse.
[tex]\text{Cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that FE is adjacent side of angle E, so:
[tex]\text{Cos(E)}=\frac{\text{FE}}{\text{DE}}[/tex]
Therefore, cos E has the same value as sin D and option 'C' is the correct choice.
