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 8m .Find the height of the tree.​

Answer 1

$\huge{\underline{\bf{\purple{Question:-}}}}$

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 8m .Find the height of the tree.

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$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ Height of the tree = 8√3.

$\large{\underline{\bf{\blue{Explanation:-}}}}$

Let the tree = AD

Let the broken part of the tree = BC

Remain part of the tree = AC

$\large{\underline{\bf{\green{Given:-}}}}$

✰ Broken part touches the ground and makes an angle 30°

✰ The distance between the foot of the tree to the point where the top touches the ground is 8m.

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the height of the tree.

$\huge{\underline{\bf{\red{Solution:-}}}}$

In ∆ ABC

Cot 30° = $\frac{AB}{AC}=\frac{B}{P}$

$:\implies\:$⠀⠀⠀√3 = 8/AC

$:\implies\:$⠀⠀⠀⠀AC√3 = 8

$:\implies\:$⠀⠀⠀AC = 8/√3

again In ∆ ABC

cos 30°= $\frac{AB}{BC}=\frac{B}{H}$

$:\implies\:$⠀⠀⠀⠀√3/2 = 8/y

$:\implies\:$⠀⠀⠀⠀y√3 = 16

$:\implies\:$⠀⠀⠀⠀y = 16/√3

Now height of tree = x + y

$:\implies\:$⠀⠀⠀⠀8/√3 + 16/√3

$:\implies\:$⠀⠀⠀⠀24 /√3

Now rationalising the denominator

$:\implies\:$⠀⠀⠀⠀24 /√3 × √3/√3

$:\implies\:$⠀⠀⠀⠀(24√3)/3

$:\implies\:$⠀⠀⠀⠀8√3

so the height of the tree = 8√3

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