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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 _____

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