Question

A tree is broken by the wind but does not separate. If the point from where it breaks is 9 m above the ground and its top touches the ground at a distance of 12 m from its foot, find out the total height of the tree before it broke.

Answer 1

Let BD be the height of the tree broken at point C and suppose CD take the position CA




Now as per given conditions we have AB = 9 m , BC = 12 m

By Pythagoras theorem:
${\mathrm{AC}}^2={\mathrm{AB}}^2+{\mathrm{BC}}^2$

$$\begin{gathered} \Rightarrow {\mathrm{AC}}^2={12}^2+9^2 \\ \Rightarrow {\mathrm{AC}}^2=144+81 \\ \Rightarrow {\mathrm{AC}}^2=225 \\ \Rightarrow {\mathrm{AC}}^2={15}^2 \\ \Rightarrow \mathrm{AC}=15 \end{gathered}$$

Length of the tree before it broke = AC + AB
= 15 + 9
= 24 m