Question

A pole being broken by the wind , the top struck the ground at an angle of 30Ëš and at a distance of 21m from the foot of the pole. Find the total height of the pol

Answer 1

Please see the attachment

Answer 2

$Let \: the \: initial \: height \: pole \: be \: AC ,\\when \:the \:wind\: come , \: the \: pole \: broke \\from \: point \:B .$

$The \:broken \: part \:of \:the \:pole \: BC \\touches \: the \: ground \:at \: D ,\: making \:an \\angle \: 30\degree \: on \:the \: ground .$

$AD = 21 \:m$

$In \:right \: angled \: \triangle BAD$

$tan 30 \degree = \frac{AB}{AD}$

$\implies \frac{1}{\sqrt{3}} = \frac{AB}{AD}$

$\implies AB = \frac{21 }{\sqrt{3} } \:m$

$In \: \triangle BAD , \: cos 30\degree = \frac{AD}{BD}$

$\implies \frac{\sqrt{3}}{2} = \frac{21}{BD}$

$\implies BD = \frac{42}{\sqrt{3}} \: m$

$But \: BD = BC$

$AD = AB + BC \\= \frac{21 }{\sqrt{3} } + \frac{42}{\sqrt{3}}\\= \frac{ 21+42}{\sqrt{3}} \\= \frac{63}{\sqrt{3}} \\= \frac{63 \sqrt{3}}{3} \\= 21\sqrt{3} \: m$

Therefore.,

$\red { Height \:of \:the \:pole } \green {= 21\sqrt{3} \: m}$

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