AMC 12 2012b Problem 25

Let $S=\{(x,y) : x\in \{0,1,2,3,4\}, y\in \{0,1,2,3,4,5\},\text{ and } (x,y)\ne (0,0)\}$. Let $T$ be the set of all right triangles whose vertices are in $S$. For every right triangle $t=\triangle{ABC}$ with vertices $A$, $B$, and $C$ in counter-clockwise order and right angle at $A$, let $f(t)=\tan(\angle{CBA})$. What is $$\prod_{t\in T} f(t)?$$

==See also==

\textbf{(A)}\ 1 \textbf{(B)}\ \frac{625}{144} \textbf{(C)}\ \frac{125}{24} \textbf{(D)}\ 6 \textbf{(E)}\ \frac{625}{24}