Question

A tree is broken at a height of 5m from the ground and its top

touches the ground at a distance of 12m from the base of the tree. Find

the original height of the tree.​

Answer 1

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Kindly refer the attachment.

✦ A'B is the height of tree.

CA is the broken part of the tree.

Hence , height of tree = CB + CA

∆ABC is right angled at B.

⋆⋆⋆ By Pythagoras theorem ,

➣ CA² = AB² + BC²

➣ CA² = 12² + 5²

➣ CA² = 144 + 25

➣ CA² = 169

➣ CA = 13m

Height of tree = CB + CA = 5 + 13

Hence , height of tree is 18m.

Answer 2

Question

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

Answer

A tree gets broken at height c of 5m from the ground.

Distance between ground and tree = 12m

using Pythagoras theory-

$\green{⊙}$(H)² = (B)² + (P)²

$\green{⊙}$(AC)² = (AB)²+(BC)²

$\green{⊙}$(AC)² = (12)² + (5)²

$\green{⊙}$(AC)²=169

$\green{⊙}$(AC)²=$\sqrt{169}$

$\green{⊙}$AC=(169)½

$\green{⊙}$=((13)²)½

$\green{⊙}$AC=13

$\green{⊙}$AC= CD =13m

The original height of the tree = BC + CD

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ =5 +13

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=18 m