Question

In ADEF, sin D = 3. What is cos E?390 15OA. 3915OB. 36O C. 99O D. 35039

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given ratio

`\begin{gathered} \sin D=(36)/(39) \\ This\text{ shows that:} \\ sin\theta=(opp)/(hyp) \\ opp=36,hyp=39 \end{gathered}`

STEP 2: Write the ratio for CAH

`\begin{gathered} \cos\theta=(adj)/(hyp) \\ hyp=39,adj=? \end{gathered}`

We solve for adjacent using pythagoras theorem

`\begin{gathered} adj^2=39^2-36^2 \\ adj=√(225)=15 \end{gathered}`

Therefore, the value of cos E will be given as:

`CosE=(adj)/(hyp)=(36)/(39)`

Answer is 36/39