Mashaal Masha
$RS=440$

$ST=384$

$TR=584$

The side lengths of right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$ . What is the value of $\tan W$?
Difficulty: Hard
A: 

$\frac{48}{73}$

B: 

$\frac{55}{73}$

C: 

$\frac{48}{55}$

D: 

$\frac{55}{48}$