삼각형의 삼각비 값 구하기

문제

다음 그림과 같이 $\overline{\text{AB}}=8$, $\overline{\text{BC}}=5\sqrt{2}$, $\angle\text{B}=45^\circ$인 삼각형 $\text{ABC}$가 있다. $\tan\text{C}$의 값은?

\begin{tikzpicture} \coordinate (A) at (0,0); \coordinate (B) at (8,0); \coordinate (H) at (5,0); % Point H on AB such that CH is altitude \coordinate (C) at (5,5); \draw (A) node[left] {A} -- (B) node[right] {B} -- (C) node[above right] {C} -- cycle; \draw (C) -- (H); \draw (H) rectangle +(0.2,0.2); % Right angle symbol at H \node at ($(A)!0.5!(B)$) [below] {$8$}; \node at ($(B)!0.5!(C)$) [above right] {$5\sqrt{2}$}; \pic [draw, angle radius=0.7cm, "{$45^\circ$}" ] {angle = C--B--A}; \end{tikzpicture}