A tree of height h m is broken by a storm in such a way that its top touches the ground at a distance of d m from its root. Find the height at which it is broken.

\(\frac{h^2 - d^2}{2h}\)

let, AB = unbroken height of tree = h

C is the point of break

let, BC = x

using Pythagoras theorem;

(A'C)² = (BC)² + (A'C)²

(h - x)² = d² + x²

⇒ h² - 2 hx + x² = d² + x²

⇒  2 hx = h² - d²

x = \(\frac{h^2 - d^2}{2h}\)