Using the trigonometric functions in a right triangle,
[tex]\begin{gathered} \cos =\frac{adjacent}{\text{hypotenuse}} \\ \tan =\frac{opposite}{\text{adjacent}} \\ \sin =\frac{opposite}{\text{hypotenuse}} \end{gathered}[/tex]
The right triangle can be resketched to get the third unknown angle;
[tex]\begin{gathered} 90+35+\theta=180^0\text{ (sum of angles in a triangle)} \\ 125^0+\theta=180^0 \\ \theta=180-125 \\ \theta=55^0 \end{gathered}[/tex]
Considering angle 55 degrees as a reference,
side y is the adjacent and side 20 is the hypotenuse.
Thus, the trigonometric identity that combines adjacent and hypotenuse is cosine.
Therefore,
[tex]\begin{gathered} \cos =\frac{\text{adjacent}}{\text{hypotenuse}} \\ \cos (55)=\frac{y}{20} \end{gathered}[/tex]
Thus, the first option is correct.
