# a tree is broken at a height of 3 m from the ground and its top touches the ground at a distance of 4 m from the base of the tree. find the original height of the tree?

Dear Student

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,

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

AC^{2} = (3 m)^{2} + (4 m)^{2}

AC^{2} = 9 m^{2} + 16 m^{2} = 25 m^{2}

AC = 5 m

Thus, original height of the tree = AC + CB = 5 m + 3 m = 8 m

Regards

**
**