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?
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 = (3 m)2 + (4 m)2
AC2 = 9 m2 + 16 m2 = 25 m2
AC = 5 m
Thus, original height of the tree = AC + CB = 5 m + 3 m = 8 m