question_answer 17)

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

Answer:

\[\text{AC}=\text{CD}\]                               \[\left| ~\text{Given} \right.\] In right angled triangle DBC, \[D{{C}^{2}}=B{{C}^{2}}+B{{D}^{2}}\] \[\left| \text{by Pythagoras Property} \right.\]                        \[={{\text{5}}^{\text{2}}}+\text{1}{{\text{2}}^{\text{2}}}\]                                          \[=\text{25}+\text{144}\]                                      \[=\text{169}\]                                                   \[\Rightarrow \]               \[DC=13\]                 \[\Rightarrow \]               \[AC=13\]                 \[\Rightarrow \]               \[AB=AC+BC=13+5=18\] Therefore, the original height of the tree \[=\text{18 m}\].