question_answer

The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, what is the actual height of the tree?

A)  \[20\,m\]           

B)         \[25\,m\]  

C)  \[30\,m\]           

D)         \[17\,m\]

Correct Answer: B

Solution :

  Since \[\Delta ABC\] is right angled,                 \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] \[\Rightarrow \]               \[A{{C}^{2}}={{8}^{2}}+{{15}^{2}}=289\] \[\Rightarrow \]               \[AC=\sqrt{289}=17\,m\] \[\therefore \] Actual length of tree                         \[=AB+AC=25m\]