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The vertical ...

Question

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 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

476.92

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Solution

The correct option is A 476.92

$R L_{T} = 450 + 0.555 + (60 + D) t a n 10.5 . . . . . . (1)$

$A l s o R L_{T} = 450 + 2.555 + D t a n 16.5 . . . . . . (2)$

From (1) and (2) , we get

$0.555 + (60 + D) t a n 10.5 = 2.555 + D t a n 16.5$

$\Rightarrow D = \frac{2 - 60 t a n 10.5}{t a n 10.5 - t a n 16.5}$

$\Rightarrow D = 82.258 m$

$\Rightarrow R L_{T} = 450 + 0.55 + 26.366$

$R L_{T} = 476.92$

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