Verify each option
Option A
Find out sinD
Calculate the length side KD (the hypotenuse of the right triangle)
Applying the Pythagorean Theorem
[tex]\begin{gathered} KD^2=24^2+31^2 \\ KD^2=1,537 \\ KD=\sqrt{1,537} \end{gathered}[/tex]
so
[tex]sinD=\frac{24}{\sqrt{1,537}}\text{ ----> by SOH}[/tex]
Option A is not true
Option B
Find out tanD
[tex]tanD=\frac{24}{31}\text{ ----> by TOA}[/tex]
Option B is not true
Option C
Find out tanK
[tex]tanK=\frac{31}{24}\text{ ----> by TOA}[/tex]
Option C is correct
Option D
Find out cosK
[tex]cosK=\frac{24}{\sqrt{1,537}}--->\text{ by CAH}[/tex]
Option D is not true
Therefore
The answer is option C
