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Answer :

Let AB be the original height of the tree and broken at C touching the ground at D such that

AC = 5 m

and AD = 12 m

In right triangle \(\triangle \)CAD,

\(AD^2 + AC^2 = CD^2 \) (By Pythagoras property)

Or, \( (12)^2 + (5)^2 = CD^2 \)

Or, 144 + 25 =\( CD^2 \)
Or, 169 = \( CD^2\)

\(\therefore \)CD =\(\sqrt{169} \) = 13 m

But CD = BC

AC + CB = AB

5 m + 13 m = AB

\(\therefore \) AB = 18 m .

Thus, the original height of the tree = 18 m.

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