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Question

A 32 meter tall areca palm snapped at a point 15 meters from the ground and its top now touches the ground. How far from the foot of the tree is its top now, on the ground?

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Solution

The given tree can be shown by a triangle as follows.

Total height of the tree = AB + AC = 32 m

Given AB = 15 m

⇒ 15 m + AC = 32 m

⇒ AC = 32 m 15 m = 17 m

Now, by using Pythagoras’ Theorem, we have

(BC)2 = (AC)2 − (AB)2

⇒ (BC)2 = (17 m)2 − (15 m)2

⇒ (BC)2 = (289 − 225) m2

⇒ (BC)2 = 64 m2

⇒ BC =

⇒ BC = 8 m

Thus, the top of the tree is 8 m from the foot of the tree.


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