Question

atri broke at a point but did not separate. its top touched the ground at a distance. it its top touched the ground at a distance of 60 m from its base. if the point where it broke be an a height 2.5 d m from the ground, what was the total height of the tree before it broke?​

Answer 1

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let ABC represent the tree before it broke at the point C, and let the top A touch the ground at A' after it broke.Then,∆ A'BC is a right triangle, right angled at B such that

A'B=6 dm , BC=2.5 dm

$\large \bold{\underline{\sf{\blue{using\: Pythagoras\:theorem\:in\:∆A'BC,\:we\:have}}}}$

(A'C)²=(A'B)²+(BC)²

➡️(A'C)²=6²+(2.5)³

➡️(A'C)²=36+6.25

➡️(A'C)²=42.5

➡️(A'C)²=(6.5)²

➡️A'C=6.5

➡️AC=A'C=6.5 dm⠀⠀⠀⠀⠀⠀[Ac=A'C]

AB=AC+BC=(6.5+2.5)dm = 9 dm

hence,the height of the tree before it broke was 90 dm

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${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{</p><p>~AngelicCandy♡ :)}}}}}}$

Answer 2

━━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\mathcal{\purple{A}\pink{N}\purple{S}\pink{W}\purple{E}\pink{R}\purple{:}\pink{:}}}$

let ABC represent the tree before it broke at the point C, and let the top A touch the ground at A' after it broke.Then,∆ A'BC is a right triangle, right angled at B such that

A'B=6 dm , BC=2.5 dm

$\large \bold{\underline{\sf{\blue{using\: Pythagoras\:theorem\:in\:∆A'BC,\:we\:have}}}}$

(A'C)²=(A'B)²+(BC)²

➡️(A'C)²=6²+(2.5)³

➡️(A'C)²=36+6.25

➡️(A'C)²=42.5

➡️(A'C)²=(6.5)²

➡️A'C=6.5

➡️AC=A'C=6.5 dm⠀⠀⠀⠀⠀⠀[Ac=A'C]

AB=AC+BC=(6.5+2.5)dm = 9 dm

hence,the height of the tree before it broke was 90 dm

━━━━━━━━━━━━━━━━━━━━━━━━━

${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{</p><p>~CandyFloss♡ :)}}}}}}$