A tree is broken by wind. if the point from where it broke is 6m above the ground and its top touches the ground at a distance of 8m from its foot. Find the total height of the tree before it broke.

Here C is the point where tree broke such that AC = 6 m

Now using pythagoreous theorem in triangle BAC we have;

${\left(\mathrm{BC}\right)}^{2}={\left(\mathrm{AC}\right)}^{2}+{\left(\mathrm{AB}\right)}^{2}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{BC}=\sqrt{{6}^{2}+{8}^{2}}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{BC}=\sqrt{100}=10$

Now CD = BC = 10 m

So the height of the tree = AC + CD = 6 m + 10 m = 16 m

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