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 \[=\text{18 m}\].
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