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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 - Mathematics

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.

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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 ΔA'BC

BC/A'C = tan 30º

BC/8 = 1/ sqrt3

`BC = (8/sqrt3)m`

A'C'/A'B =  cos 30º

`8/(A'B) = sqrt3/2`

`A'B =  ((16)/sqrt3)m`

Height of tree = A'B+BC

`=(16/sqrt3+8/sqrt3)m = 24/sqrt3 m`

`= 8sqrt3m`

Hence the height of the tree is `8sqrt3 m`

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APPEARS IN

NCERT Class 10 Maths
Chapter 9 Some Applications of Trigonometry
Exercise 9.1 | Q 2 | Page 203
RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 19 | Page 30
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