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The angle of elevation of the top of tower as observed from a point on the horizontal ground is 'x' if we move a distance 'd' towards the foot of the tower the angle of elevation increases to 'y' then find the height of the tower.

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\frac{dtanxtany}{tany - tanx}

d (tany + tanx)

d (tany - tanx)

\frac{dtanxtany}{tany + tanx}

answer is A.

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Detailed Solution

Given is a tower.
From its top, the angle of elevation is x.
If we move a distance 'd' towards the foot of the tower the angle of elevation increases to 'y'.
Question Image

Let the height of the tower be h.

∴

ΔABC

tany = \frac{h}{b}

\Rightarrow

b =

\frac{h}{tany}

ΔABD,

tanx = \frac{h}{b + d}

\Rightarrow tanx = \frac{h}{\frac{h}{tany} + d}

\Rightarrow \frac{h}{tany} + d = \frac{h}{tanx}

\Rightarrow d =

h (\frac{1}{tanx} - \frac{1}{tany})

\Rightarrow d =

h (\frac{tany - tanx}{tanxtany})

\Rightarrow h =

\frac{dtanxtany}{tany - tanx}

So, the height of tower is

\frac{dtanxtany}{tany - tanx} .

Hence, the correct option is 1.

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