The missing sides, x, and y can be obtained using the sine rule
Step 1: Get the angle at A
The angle at A is obtained below:
[tex]180-90-45=45^0[/tex]
Step 2: Use the sine rule
[tex]\frac{\sin A}{y}=\frac{\sin B}{x}=\frac{\sin C}{5}[/tex]
[tex]\begin{gathered} \text{where A=45}^0 \\ B\text{=45}^0 \\ C=90^0 \end{gathered}[/tex]
To get y
[tex]\frac{\sin45}{y}=\frac{\sin 90}{5}[/tex]
cross multiply
[tex]y=\frac{5\times\sin 45}{\sin 90}=\frac{5\sqrt[]{2}}{2}[/tex]
To get x
[tex]\frac{\sin45}{x}=\frac{\sin 90}{5}[/tex][tex]x=\frac{5\times\sin 45}{\sin 90}=\frac{5\sqrt[]{2}}{2}[/tex]
Therefore, the answer is option C
