The vertical angles subtended by the top of a tower T at two instrument stations set up at P and Q, are shown in the figure. The two stations are in line with the tower and spaced at a distance of $60$ m. Readings taken from these two stations on a leveling staff placed at the benchmark ($BM=450.000$ m) are also shown in the figure. The reduced level of the top of the tower T (expressed in m) is _____