Question

V60°
Q.7 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

• Original height of tree is 18 cm.

Step-by-step explanation:

Given:-

• A tree is broken at a height of 5 m .
• Its top touches the ground at a distance of 12 m from the base of the tree.

To find:-

• Original height of tree.

Solution:-

Let, A tree is broken at a height be AB

And, Its top touches the ground at a distance be BC and AC be length broken tree.

AB = 5 m

BC = 12 cm.

AC = ?

Using Pythagoras theorem,

$\sf \star \: \bold{ {Hypotenuse}^{2} = {Height}^{2} + {Base}^{2} }$

$\longrightarrow \sf {AC}^{2} = {AB}^{2} + {BC}^{2}$

$\longrightarrow \sf {AC}^{2} = {(12)}^{2} + {(5)}^{2}$

$\longrightarrow \sf {AC}^{2} =144 + 25$

$\longrightarrow \sf {AC}^{2} = 169$

$\longrightarrow \sf AC = \sqrt{169}$

$\longrightarrow \sf \bold{AC = 13}$

We have taken broken tree be AC So, length broken tree is 13 m.

Original height = Length of broken tree + Height from where tree broken.

$\longrightarrow \sf 13 + 5$

$\longrightarrow \sf 18$

Therefore,

Original height of tree is 18 m.