Question : The top of a broken tree touches the ground at a distance of 15 metres from its base. If the tree is broken at a height of 8 metres from the ground, then the actual height of the tree is:
Option 1: 17 metres
Option 2: 20 metres
Option 3: 25 metres
Option 4: 30 metres
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Correct Answer: 25 metres
Solution : Given: The top of a broken tree touches the ground at a distance of 15 metres from its base and the tree is broken at a height of 8 metres from the ground. Let h be the actual height of the tree. From the figure we get, BD = 8 metres, BC = 15 metres and AD = CD = (h – 8) metres. By using the Pythagoras theorem, CD 2 = BD 2 + BC 2 ⇒ (h – 8) 2 = 8 2 + 15 2 ⇒ (h – 8) 2 = 289 ⇒ (h – 8) = 17 ⇒ h = 17 + 8 ⇒ h = 25 Hence, the correct answer is 25 metres.
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