To calculate x, we will use the trigonometry ratio
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenus} \\ \text{where,} \\ \text{opposite =opp=x} \\ \text{hypotenus}=\text{hyp}=5 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \sin 45^0=\frac{x}{5} \\ x=5\times sin45^0 \\ x=5\times\frac{\sqrt[]{2}}{2} \\ x=\frac{5\sqrt[]{2}}{2} \end{gathered}[/tex]
To calculate y, we will use the trigonometric ratio,
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenus} \\ \text{where,} \\ \text{adjacent}=\text{adj}=y \\ \text{hypotenus}=\text{hyp}=5 \\ \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \cos 45^0=\frac{y}{5} \\ y=5\times\cos 45^0 \\ y=5\times\frac{\sqrt[]{2}}{2} \\ y=\frac{5\sqrt[]{2}}{2} \end{gathered}[/tex]
Hence,
The correct answer is OPTION C
