The distance between two poles of equal heigh | vedclass

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Question

(C) Let $\overline{AB}$ and $\overline{ED}$ be two poles of equal height $h \, m$ and $C$ be the point of observation on the line segment $\overline{B

Vedclass · Accepted Answer

$86.5$

Vedclass · Answer

(C) Let $\overline{AB}$ and $\overline{ED}$ be two poles of equal height $h \, m$ and $C$ be the point of observation on the line segment $\overline{BD}$ joining the bases of the poles.Given $BD = 200 \, m$. Let $BC = x \, m$,then $CD = (200 - x) \, m$.The angles of elevation are $\angle ACB = 60^{\circ}$ and $\angle ECD = 30^{\circ}$.In $	riangle ABC$,$	an 60^{\circ} = \frac{AB}{BC} \implies \sqrt{3} = \frac{h}{x} \implies x = \frac{h}{\sqrt{3}} \quad \dots(1)$In $	riangle EDC$,$	an 30^{\circ} = \frac{ED}{CD} \implies \frac{1}{\sqrt{3}} = \frac{h}{200 - x} \implies 200 - x = \sqrt{3}h \implies x = 200 - \sqrt{3}h \quad \dots(2)$Equating $(1)$ and $(2)$:$\frac{h}{\sqrt{3}} = 200 - \sqrt{3}h$$h = 200\sqrt{3} - 3h$$4h = 200\sqrt{3}$$h = 50\sqrt{3} \approx 50 	imes 1.732 = 86.6 \, m$ (Using $\sqrt{3} \approx 1.732$,the closest option is $86.5 \, m$).

The distance between two poles of equal height is $200 \, m$. From a point situated on the line segment joining their bases,the angles of elevation of their tops are found to be $60^{\circ}$ and $30^{\circ}$. Find the height of the pole in $m$.

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