Question
A tree is broken by the wind but does not separate. If the point from where it breaks is $9m$ above the ground and its top touches the ground at a distance of $12m$ from its foot, find out the total height of the tree before it broke.
✓
Answer
Let $A B$ be the tree which broke at $D$ and its top $A$ touches the ground at $C$.
Their $B D=5 \mathrm{~m}$ and $\mathrm{BC}=12 \mathrm{~m}$
Let $A D=x m$, then $C D=x m$
Now, in right $\triangle \mathrm{ABC}$,
$C D^2=B D^2+\mathrm{BC}^2(\text { By Pythagoras Theorom })$
$C D^2=(9)^2+(12)^2$
$\Rightarrow C D^2=81+144$
$\Rightarrow C D^2=225$
$\Rightarrow C D^2=(15)^2$
$C D=15 \mathrm{~m}$
$A D=x=15 \mathrm{~m}$
Height of the tree $A B=A D+B D=15+9=24 m$.
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