To obtain the missing lengths x and y, we would have to use the sine and cosine relations;
[tex]\begin{gathered} x=24\sin 30 \\ x=24\times0.5 \\ x=12 \end{gathered}[/tex]
We can move to y;
[tex]\begin{gathered} y=24\cos 30 \\ y=24\times0.8660 \\ y=20.78 \end{gathered}[/tex]
Therefore, the missing lengths are x = 12 and y = 20.78
Part B
We need to find x, x is opposite the 45-degree angle, therefore, we can use the sine relationship;
[tex]\begin{gathered} x=12\sin 45 \\ x=12(\frac{1}{\sqrt[]{2}})=\frac{12}{\sqrt[]{2}}\text{ or 6}\sqrt[]{2} \end{gathered}[/tex]
Therefore, the correct options are A and E
