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Question 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.


Solution

Let A’CB represents the tree before it broke at the point C and let the top ‘A’ touches the ground at A after it broke.
Then ΔABC  is a right-angled triangle, right angled at B.
AB = 12 m and BC = 5m
Using Pythagoras theorem, In Δ ABC

(AC)2=(AB)2+(BC)2(AC)2=(12)2+(5)2(AC)2=144+25(AC)2=169AC=13 mHence, the total height of the tree = AC + CB = 13 + 5 = 18 m.

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