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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.
Solution
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.
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