Question

a tall tree is broken by a storm. it brokes at apoint but did not separate. its top reaches the ground at a distance 40 m from the base. if the height of the point from which the tree broke is 9m from the ground, find the initial height of the tree​

Answer 1

Step-by-step explanation:

The initial height of the tree was 50 metre.

Answer 2

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.

Hope it helps you...