In the following figure, triangle \(ABC\) is similar to triangle \(DEF\). What is the value of \(\tan{E}\)?

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Because the triangles are similar, the measure of the corresponding angles of both triangles will be congruent.

Therefore, since \( m\angle{E}=m\angle{B},   \tan{E}=\tan{B}\).

$$ \tan{B}=\frac{\text{opposite}}{\text{adjacent}} $$ $$= \boxed{\frac{5}{12}} $$