Question

A tall tree is broken by a storm. It broke at a point but did not separate. It's top reaches the ground, at a distance 40 m from its base. If the height of the point from which the tree broke, is 9 m from the ground, find the initial height of the tree.
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Answer 1

Let AB be the tree and P be the point at which it got broken. Let Q be the point where the top of the tree touched the ground.

Then, we have:

PB = PQ, AP = 9m, QA = 40m. In right ∆APQ, we have : ∠A = 90°.

By Pythagoras’ Theorem:

PQ² = QA² + AP² = (40² + 9²) m² = (1600 + 81) m²

= 1681 m² = (41 m)²

∴ PQ = 41 m.

And so, PB = PQ = 41 m.

Now, AB = AP + PB = 9m + 41 m = 50 m.

Hence, the height of the tree before it was broken = 50 m.