Question

Q12. A tree is broken at a height of 8m from the ground and its top touches the ground at a distance of 15m from the base of the tree. Find the original height of the tree. ​

Answer 1

Given :

• A tree is broken at a height of 8 m from the ground and its top touches the ground at a distance of 15m from the base of the tree .

To Find :

• Original Height of the tree .

Solution :

$\longmapsto\tt{AB=8\:m}$

$\longmapsto\tt{BC=15\:m}$

Using Pythagoras Theorem :

$\longmapsto\tt\bf{{(AC)}^{2}={(AB)}^{2}+{(BC)}^{2}}$

$\longmapsto\tt{{(AC)}^{2}={(8)}^{2}+{(15)}^{2}}$

$\longmapsto\tt{{(AC)}^{2}=64+225}$

$\longmapsto\tt{{(AC)}^{2}=289}$

$\longmapsto\tt{AC=\sqrt{289}}$

$\longmapsto\tt\bf{AC=17\:m}$

Now ,

Original Height of Tree :

$\longmapsto\tt{8+17}$

$\longmapsto\tt\bf{25\:m}$

So , The Original Height of the tree is 25 m .

Answer 2

$\large\underline{\underline{\maltese{\color{darkblue}{\pmb{\sf{\: Given :-}}}}}}$

• ➬ A tree is broken at a height of 8m from the ground .
• ➬ Its top touches the ground at the distance of 15m from the base of the tree.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\underline{\maltese{\pink{\pmb{\sf{\: To \: Find :-}}}}}}$

• ➬ Original height of the tree = ?

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\underline{\maltese{\orange{\pmb{\sf{\: Solution :-}}}}}}$

❒ Formula Used :

$\large{\blue{\bigstar}}{\underline{\boxed{\red{\sf{ (Hypetenuse)² = (Base) ² + (Height)²}}}}}$

➢Here :

• ➳ Hypotenuse = ?
• ➳ Base = 15 m
• ➳ Height = 8 m

$\qquad{━━━━━━━━━━━━━━━}$

❒ Hypotenuse :

${:\longmapsto{\sf{ Hypotenuse² = Base² + Height²}}}$

${:\longmapsto{\sf{ Hypotenuse² = 15² + 8²}}}$

${:\longmapsto{\sf{ Hypotenuse² = 225+ 64}}}$

${:\longmapsto{\sf{ Hypotenuse² = 289}}}$

${:\longmapsto{\sf{ Hypotenuse= \sqrt{289} }}}$

$\large\qquad{\color{maroon}{:\longmapsto{\underline{\boxed{\sf{ Hypotenuse = 17 \: m}}}}}}{\pink{\bigstar}}$

❒ Original Height of tree :

${:\longmapsto{\sf{ Original Height_{(Tree) } = Hypotenuse + Height }}}$

${:\longmapsto{\sf{ Original Height_{(Tree) } = 17+ 8}}}$

$\large\qquad{\color{green}{:\longmapsto{\underline{\boxed{\sf{Original \: Height = 25 m }}}}}}{\pink{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Original height of tree is 25 m. ❞

${\blue{\underline{▬▬▬▬▬}}{\pink{\underline{▬▬▬▬▬}}{\orange{\underline{▬▬▬▬▬}}{\purple{\underline{▬▬▬▬▬▬}}}}}}$