ANSWER
RS = 2
EXPLANATION
Using SOH CAH TOA
[tex]\begin{gathered} \text{ sin }\theta\text{ = }\frac{Opp}{Hyp} \\ sin45^0\text{ = }\frac{RS}{2\sqrt[]{2}} \\ \text{ Recall: sin }45^0\text{ = }\frac{1}{\sqrt[]{2}} \\ \frac{1}{\sqrt[]{2}}\text{ = }\frac{RS}{2\sqrt[]{2}} \\ \text{ Cross multiply} \\ \sqrt[]{2}\text{ RS = 2}\sqrt[]{2} \\ \text{ Divide through by }\sqrt[]{2} \\ \frac{\sqrt[]{2}\text{ RS}}{\sqrt[]{2}}\text{ = }\frac{2\sqrt[]{2}}{\sqrt[]{2}} \\ RS\text{ = 2} \end{gathered}[/tex]
Hence, RS is 2
