Question

Which of the following is correct based on this picture? A. sinD=3124B. tanD=3124C. tanK=3124D. cosK=3124

Answer 1

Verify each option

Option A

Find out sinD

Calculate the length side KD (the hypotenuse of the right triangle)

Applying the Pythagorean Theorem

$\begin{gathered} KD^2=24^2+31^2 \\ KD^2=1,537 \\ KD=\sqrt{1,537} \end{gathered}$

so

$sinD=\frac{24}{\sqrt{1,537}}\text{ ----> by SOH}$

Option A is not true

Option B

Find out tanD

$tanD=\frac{24}{31}\text{ ----> by TOA}$

Option B is not true

Option C

Find out tanK

$tanK=\frac{31}{24}\text{ ----> by TOA}$

Option C is correct

Option D

Find out cosK

$cosK=\frac{24}{\sqrt{1,537}}--->\text{ by CAH}$

Option D is not true

Therefore

The answer is option C