Question

A tree is broken at a height of 5 m from the ground and its top touchs the ground at a distance of 12 m from the base of the tree . find the origin /height of the tree.

Answer 1

Here, the height of the tree after the tree was broken $=5cm.$

the distance of the top of the tree to the base of the tree $=12m$

In $\Delta AOB$ where $O$ is at right-angled

using Pythagoras Theorem,

$A{O}^2+O{B}^2=A{B}^2$

$(5{)}^2+(12{)}^2=A{B}^2$

$\Rightarrow AB=\sqrt{25+144}=\sqrt{169}$

$\Rightarrow AB=13m$

and $AB=CA$

$\Rightarrow AC=13m$

Original Height of the tree $=AC+AO$

$=13+5$

$=18m$