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?

Answer 1

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.