Question

2. A tree is broken at a height of 9 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. (3 marks)
a​

Answer 1

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Let A'CB represents the tree before it broken 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=12m and BC=5m

Using Pythagoras theorem, In ΔABC

(AC)2+(AB)2+(BC)2

⇒(AC)2=(12)2+(5)2

⇒(AC)2=144+25

⇒(AC)2=169

⇒AC=13m

Hence, the total height of the tree=AC+CB=13+5=18m.