Question

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.​

Answer 1

GIVEN :-

• tree is broken from 5 m height

• distance between top of tree and foot of tree after breaking is 12 m

TO FIND :-

• original height of tree

FIGURE :-

• reffered to the attachment

SOLUTION :-

Let A'CB represents the tree before it broken at the point C and let the top A' touches the ground at A after it broke. Then ΔABC is a right angled triangle, right angled at B.

AB = 12m and BC = 5m

now we know that in PYTHAGORAS THEOREAM:-

$\implies \boxed{ \rm{ {h \: }^{2} = {b}^{2} + {p}^{2} }}$

where

• h = hypotenuse

• b = base

• p = perpendicular

therefore according to PYTHAGORAS THEOREAM

$\implies \rm{ {(ac)}^{2} = {(ab)}^{2} + {(bc)}^{2} }$

$\implies \rm{ {(ac)}^{2} = {(12)}^{2} + {(5)}^{2} }$

$\implies \rm{ {(ac)}^{2} = 144 + 25}$

$\implies \rm{ {(ac)}^{2} = 169}$

$\implies \rm{ \sqrt{{(ac)}^{2} \: } = \sqrt{ 169}}$

$\implies \rm{ \bold{ac = 13 \: m}}$

now we know that ,

total height of tree = AC + BC

$\implies \rm{13 + 5 }$

$\implies \rm{18 \: m}$

$\implies \boxed{ \boxed{ \rm{total \: height \: of \: tree \: = 18 \: m}}}$

OTHER INFORMATION :

Pythagoras Theorem Statement :

• Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.