Question

A tree is broken at a height of 5 m from the ground and its top touches 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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$\text{\large\underline{\purple{Solution:-}}}$

let the original height of tree BD and tree is broken at point c; at a height of 5m from the ground let tip of the tree the touches the ground at point A, 12 m away from the base of the tree.

since it form a right - angled triangle; ᐃABC right angled at point B.

Now using Pythagoras property,

⠀⠀⠀$\bold{⇒ AC² = AB² + BC²}$

⠀⠀⠀$\bold{⇒12² + 5²}$

⠀⠀⠀$\bold{⇒ 144 + 25}$

⠀⠀⠀$\bold{⇒AC² = 169}$

⠀⠀⠀$\implies \sf{\sqrt{169}}$

⠀⠀⠀$\bold{⇒AC = 13m}$

original height of tree $\bold{ = BC + CA}$

$\bold{= 5m + 13m = 18m}$

Hence, original height of the tree is 18 m.

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Answer 2

Since it form a right - angled triangle; ᐃABC right angled at point B.

Now using Pythagoras property,

$\sf{⇒ AC² = AB² + BC²}$

$\sf{⇒12² + 5²}$

$\sf{⇒ 144 + 25}$

$\sf{⇒AC² = 169}$

⇒$\sf{\sqrt{169}}$

⇒AC = 13m

Original height of tree = BC + CA =BC+CA

= 5m + 13m = 18m =5m+13m=18m

Hence, original height of the tree is 18 m.