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Question
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.
Options
25 m
13 m
18 m
17 m
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Solution
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is 18 m.
Explanation:
Let BC is the broken part of tree and AB is the unbroken part of tree.
Here, ΔABC is right angled triangle.
∴ (BC)2 = (AB)2 + (AC)2
⇒ (BC)2 = (5)2 + (12)2
⇒ (BC)2 = 25 + 144 = 169
⇒ (BC)2 = 132
⇒ BC = 13 m
∴ Actual height of tree is AB + BC = (5 + 13) m = 18 m.
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