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. -
Answer & explanation
Correct answer: option 1
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