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.
Answer & explanation
Correct answer: option 3
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 = \(\frac{h^2 - d^2}{2h}\)