From two points,lying on the same horizontal | vedclass

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(C) Let $AC$ be the height of the pillar $= h \ m$.Let $B$ and $D$ be the two points on the same horizontal line such that $\angle ABC = 	heta$ and $

Vedclass · Accepted Answer

$h(\cot 	heta - \cot \phi)$

Vedclass · Answer

(C) Let $AC$ be the height of the pillar $= h \ m$.Let $B$ and $D$ be the two points on the same horizontal line such that $\angle ABC = 	heta$ and $\angle ADC = \phi$.In $	riangle ADC$,$	an \phi = \frac{AC}{CD} = \frac{h}{CD}$,so $CD = h \cot \phi$.In $	riangle ABC$,$	an 	heta = \frac{AC}{CB} = \frac{h}{CB}$,so $CB = h \cot 	heta$.The distance between the two points $B$ and $D$ is $BD = CB - CD$.Substituting the values,$BD = h \cot 	heta - h \cot \phi = h(\cot 	heta - \cot \phi)$.

From two points,lying on the same horizontal line,the angles of elevation of the top of the pillar are $\theta$ and $\phi$ $(\theta < \phi)$. If the height of the pillar is $h$ $m$ and the two points lie on the same side of the pillar,then the distance between the two points is (in $m$):

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