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=√(1,537) \end{gathered}`

so

`sinD=(24)/(√(1,537))\text{ ----> by SOH}`

Option A is not true

Option B

Find out tanD

`tanD=(24)/(31)\text{ ----> by TOA}`

Option B is not true

Option C

Find out tanK

`tanK=(31)/(24)\text{ ----> by TOA}`

Option C is correct

Option D

Find out cosK

`cosK=(24)/(√(1,537))--->\text{ by CAH}`

Option D is not true

Therefore

The answer is option C