There is enough info here to enable use of the Law of Sines to find the length of PQ. Note that this is not a right triangle; there is no 90 degree angle.
According to the Law of Sines,
length of PQ 14
--------------------- = -----------------
sin 40 deg sin 80 deg
or ...
14 sin 40 deg 8.999
length of PQ = ---------------------- = --------------- = 9.139
sin 80 deg 0.985
