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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

A property owner wants to find the length $x$, in feet, across a pond as represented in the figure. $\overline{PR}$ intersects $\overline{ST}$ at point $Q$, and $\angle PTQ$ is congruent to $\angle RSQ$. The lengths represented by $PQ,TQ,QS,$ and $RS$ were determined to be $4,200$ feet, $8,400$ feet, $1,400$ feet, and $1,600$ feet, respectively.

What is the value of $x$?

1

9600