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Question
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground, making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Solution
Let AC was the original tree. Due to storm, it was broken into two parts. The broken part A'B is making 30° with the ground.
In ΔABC
`("BC")/("AC") = tan 30º`
`("BC")/8 = 1/ sqrt3`
`"BC" = (8/sqrt3)m`
`("AC")/("AB") = cos 30º`
`8/("AB") = sqrt3/2`
`"AB" = ((16)/sqrt3)m`
Height of tree = AB + BC
= `(16/sqrt3+8/sqrt3)m`
= `24/sqrt3 m`
= `8sqrt3m`
Hence, the height of the tree is `8sqrt3 m`.
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