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Question -

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree . Find the original height of the tree.



Answer -

Let ABbe the original height of the tree and broken at C touching the ground at Dsuch that

AC = 5 m
and AD = 12 m
In right triangle ∆CAD,
AD2 + AC2 =CD2 (By Pythagoras property)
⇒ (12)2 + (5)2 =CD2
⇒ 144 +25 = CD2
⇒ 169 =CD2
∴ CD == 13 m

But CD = BC
AC + CB = AB
5 m + 13 m = AB
∴ AB =18 m .
Thus, the original height of the tree = 18 m.

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