Given the Right Triangle BCD, you know that:
[tex]\begin{gathered} BD=8 \\ m\angle BCD=63\degree \end{gathered}[/tex]
Then, you can use the following Trigonometric Function in order to find the length of the side CD:
[tex]\sin \beta=\frac{opposite}{hypotenuse}[/tex]
In this case:
[tex]\begin{gathered} \beta=63\degree \\ opposite=BD=8 \\ hypotenuse=CD \end{gathered}[/tex]
Therefore, substituting values and solving for CD, you get:
[tex]\begin{gathered} \sin (63\degree)=\frac{8}{CD} \\ \\ CD\cdot\sin (63\degree)=8 \end{gathered}[/tex][tex]\begin{gathered} CD=\frac{8}{\sin(63\degree)} \\ \\ CD\approx9.0 \end{gathered}[/tex]
Hence, the answer is:
[tex]CD=9.0[/tex]
