A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 60 degre

Question

3 years ago

15

e with the ground. The distance between the feet of the tree to the point where the top touches the ground is 16m. Find the height of the tree.

1 answer:

ladessa [460] · Answer 1 · 2023-01-22T08:37:42+03:00

The height of the triangle is 8root3 meters.

We have given that,

A tree breaks due to a storm and the broken part bends,

So that the top of the tree touches the ground making an angle of 60 degrees with the ground.

The distance between the feet of the tree to the point where the top touches the ground is 16m.

Let the Height of the Tree =AB+AD

and given that BD=8 m

Now, when it breaks a part of it will remain perpendicular to the ground (AB) and the remaining part (AD) will make an angle of 30 degrees.

Now, in △ABD

cos(30)=BD/AD=BD=root3AD/2

AD=2(8)/root3

also in the same triangle

$tan(30)=AB/BD\implies 8/\sqrt{3}$

<h3>What is the height of the triangle?</h3>

Height of the tree=AB+AD

$=\frac{16}{\sqrt{3} }+\frac{8}{\sqrt{3} } }$

$=\frac{24}{\sqrt{3} } \\=8\sqrt{3}m$

Therefore the height of the triangle is 8root3.

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