Question

upper part of the tree broken over by the wind makes an angle of 30 degree with the ground and the distance of the root from the point where the top touches the ground is 25m what was the height of the tree

Answer 1

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Answer 2

Answer:

$Height \: of \: the \: tree=43.3\:m$

Step-by-step explanation:

Let AB be the tree broken at a point C such that the broken part CB takes the position CO and strikes the ground at O.

It is given that OA = 25 m.

and <AOC = 30°.

Let AC = x and CB = y .

Then, CO = y .

$In \triangle OAC ,we \:have\\</p><p>tan 30\degree = \frac{AC}{OA}\\\implies \frac{1}{\sqrt{3}}=\frac{x}{25}$

$\implies x = \frac{25}{\sqrt{3}}\: ---(1)$

$And \\cos 30\degree = \frac{OA}{OC}$

$\implies \frac{\sqrt{3}}{2}=\frac{25}{y}$

$\implies y = \frac{50}{\sqrt{3}}\:---(2)$

$Height \: of \: the \: tree\\ = (x+y) \: m\\= \frac{25}{\sqrt{3}}+\frac{50}{\sqrt{3}}\\=\frac{25+50}{\sqrt{3}}\\=\frac{75}{\sqrt{3}}\\=\frac{75\sqrt{3}}{\sqrt{3}\times\sqrt{3}}\\=\frac{75\sqrt{3}}{3}\\=25\sqrt{3}\\=25\times 1.732\\= 43.3 \:m$

Therefore,

$Height \: of \: the \: tree=43.3\:m$

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