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Math·Geometry and Trigonometry·Right triangles and trigonometry

hard

Triangle $ABC$ is similar to triangle $DEF$, where $A$ corresponds to $D$ and $C$ corresponds to $F$. Angles $C$ and $F$ are right angles. If $\tan (A)=\sqrt{3}$ and $DF=53$, what is the length of $\overline{DE}$?

A

$53\frac{\sqrt{3}}{3}$

B

$53\frac{\sqrt{3}}{2}$

C

$53\sqrt{3}$

D

$106$