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.

In the given figure, BC represents the unbroken part of the tree. Point C represents the point where the tree broke and CA represents the broken part of the tree. Triangle ABC, thus formed, is right-angled at B.

Applying Pythagoras theorem in ΔABC,

AC2 = BC2 + AB2

AC2 = (5 m)2 + (12 m)2

AC2 = 25 m2 + 144 m2 = 169 m2

AC = 13 m

Thus, original height of the tree = AC + CB = 13 m + 5 m = 18 m

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