# The right triangle

Geometry Level pending

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 $\prod_{t\in T} f(t)?$

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