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Math·Geometry and Trigonometry·Right triangles and trigonometry

hard

Triangle $ABC$ is similar to triangle $DEF$, where angle $A$ corresponds to angle $D$ and angle $C$ corresponds to angle $F$. Angles $B$ and $E$ are right angles. If $\cos A=\frac{14}{\sqrt{421}}$, what is the value of $\frac{1}{\sin F}$?

A

$\frac{15}{\sqrt{421}}$

B

$\frac{14}{\sqrt{421}}$

C

$\frac{\sqrt{421}}{14}$

D

$\frac{\sqrt{421}}{15}$