Question

Due to a heavy storm, a part of a banyan tree broke without separating from the main. The top of the tree touched the ground 15 m from the base making an angle of 45° with the ground. Calculate the height of the tree before it was broken.

Answer 1

Let AC was original tree. Due to storm it was broken into two parts. The broken part A' B is making 45° with ground. 
In ΔA'BC

`"BC"/"A'C" = tan 45°`

`"BC"/15 = 1`

BC = 15

`"A'C"/"A'B" = cos 45°`

`15/"A'B" = 1/sqrt(2)`

`A'B = 15sqrt(2)`

`"Height of tree" = A'B + BC = 15 + 15sqrt(2) = 15(1 + sqrt(2)) = 15 × 2.414 = 36.21`

Hence , the height of tree was 36.21 m.