SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given ratio
[tex]\begin{gathered} \sin D=\frac{36}{39} \\ This\text{ shows that:} \\ sin\theta=\frac{opp}{hyp} \\ opp=36,hyp=39 \end{gathered}[/tex]
STEP 2: Write the ratio for CAH
[tex]\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ hyp=39,adj=? \end{gathered}[/tex]
We solve for adjacent using pythagoras theorem
[tex]\begin{gathered} adj^2=39^2-36^2 \\ adj=\sqrt{225}=15 \end{gathered}[/tex]
Therefore, the value of cos E will be given as:
[tex]CosE=\frac{adj}{hyp}=\frac{36}{39}[/tex]
Answer is 36/39
