Question

A tree is broken at a height of $8$m from the ground and its top touches the ground at a distance of $15$m from the base of the tree. Find the original height of the tree.

• A. $25m$
• B. $5m$
• C. $23m$
• D. $16m$

Answer 1

Answer: (A)

$25m$

Let $BD$ be the original height of tree.

$\therefore AD=AC$

In $△ABC$

$A{C}^2=A{B}^2=B{C}^2$

$={15}^2+8^2$

$=225+64$

$=289$

$\Rightarrow AC=17m$

$\Rightarrow AD=17m$

$\therefore$ Original height of tree $=(17+8)m=25m$