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

From the figure, we have

BC is the unbroken part of the tree

Point C represents that point where the tree broke

CA represents the broken part of the tree

is right angled at B

By applying pythagoras theorem, we get:

AC^{2} = BC^{2} + AB^{2}

AC^{2} = (5)^{2} + (12)^{2}

AC^{2} = 25 + 144

AC^{2} = 169 m^{2}

AC =

AC = 13 m

Hence,

The original height of the tree = AC + CB

= 13 m + 5 m

= 18 m

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