Ex 6.5, 5 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.
Given that tree breaks down
Let the part after breaking down be AB
Distance of its top from base of tree be BC
Since Tree is vertical
∠ B = 90°
and
AB = 5 m
BC = 12 m
In Δ ABC
By Pythagoras Theorem,
〖(𝐴𝐶)〗^2 = 〖(𝐴𝐵)〗^2 + 〖(𝐵𝐶)〗^2
〖(𝐴𝐶)〗^2 = 〖(12)〗^2 + 〖(5)〗^2
〖(𝐴𝐶)〗^2 = 144 + 25
〖(𝐴𝐶)〗^2 = 169
〖(𝐴𝐶)〗^2 = 〖(13)〗^2
Cancelling square
AC = 13 m
Original height of tree = AB + AC
= 5 + 13
= 18 m
∴ Original height of tree is 18 m

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.