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.
Answers
Given :-
- 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.
To Find :-
- Find the original height of the tree.
Solution :-
~Here, we’re given that 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 and we need to find the original height of the tree. The structure of a tree is forming a right-angled triangle where 5m is perpendicular and 12m is base. By applying Pythagoras theorem we can find the hypotenuse and the sum of hypotenuse and perpendicular is the original height of the tree.
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As we know that ,
★ Pythagoras theorem = h² = b² + p²
Where,
• h is hypotenuse
• b is base = 12m
• p is perpendicular = 5m
Finding hypotenuse :-
➟ h² = 12² + 5²
➟ h² = 144 + 25
➟ h² = 169
➟ h = √169
↬ h = 13 m
Finding the original length of tree :-
➟ Hypotenuse + Perpendicular
➟ 13m + 5m
↬ 18 m
Hence,
- Original height of the tree is 18 m
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Answer:
18m
Step-by-step explanation:
Let the length AC be x
We have to find. x+5
12^2+5^2=x^2. (pythagores theorem)
144+25=x^2
169=x^2
x=13m
The original height of the tree=x+5=13+5=18m
