A tree of height 75 m is broken by a storm in such a way that its top touches the ground at a distance of 25 m from its root. Find the height at which it is broken. -

33.33 m 

Let the heoght at which the tree breaks be x m above ground  i.e. BC = x

A'B = 75 - x

Using Pythagoras theorem 

(A'B)² = (BC)² + (A'C)²

(75 - x)² = (x)² + (25)²

(75)² - 150x + (x)² = (x)² + (25)²

150x = ((75)² - (25)²) 

150x = (75 + 25)(75 - 25)

150x = 100 x 50 

x = \(\frac{100}{3}\) = 33.33 m