Solution:

\(\displaystyle\triangle{A}{B}{C}\)

\(\displaystyle{{\cos{{45}}}^{\circ}=}{\frac{{{9}}}{{{x}}}}\)

\(\displaystyle{x}={\frac{{{9}}}{{{\cos{{45}}}^{\circ}}}}\)

\(\displaystyle{x}={9}\sqrt{{2}}\)

\(\displaystyle{{\sin{{45}}}^{\circ}=}{\frac{{{y}}}{{{9}\sqrt{{2}}}}}\)

\(\displaystyle{y}={9}\sqrt{{2}}{{\sin{{45}}}^{\circ}\Rightarrow}{y}={9}\)

\(\displaystyle\triangle{A}{D}{C}\)

\(\displaystyle{{\sin{{45}}}^{\circ}=}{\frac{{{9}}}{{{z}}}}\)

\(\displaystyle{z}={9}\sqrt{{2}}\)