In quadrilateral QRTS, we have QR = 11, QS = 9, and ST=2. Sides line RQ and line ST are extended past Q and S, respectively, to meet at point P. If PS = 8 and PQ = 5, then what is RT?

Answer 1

in triangle PQS.
sinP/9 = sinQ/8 = sinS/5
So, you can find angle P
Now, using the law of cosines in triangle PRT

RT^2 = 10^2 + 16^2 - 2*10*16*cos(P)

Answer 2

not sure how I'd do it without trig.

Any clever geometric relationships that make it easy?