Question

$\huge \fbox \red{❥ Question}$


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.




(REQUIRED QUALITY ANSWER )

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Answer 1

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Let the broken part of tree be AC ...

GIVEN :-

distance between foot of the tree B and point C = 8 m

So , BC = 8 m

Broken parts of tree makes an angle 30° with ground

So , ∠C = 30°

TO FIND :-

height of the tree

ANsWeR :-

Height of the tree = Height of broken part + Height of remaining tree

Height of tree = AB + AC

Since , tree was vertical to ground ...

So , ∠ABC = 90°

In Right-Angled triangle ABC ,

cos C = side adjacent to angle C / hypotenuse

cos C = BC / AC

cos 30° = 8 / AC

√3/2 = 8 / AC

AC = 8 × 2 / √3

AC = 16 / √3

In Right-Angled triangle ABC ,

sin C = side opposite to angle C / Hypotenuse

sin 30° = AB / AC

1/2 = AB / 16/√3

1/2 = √3 / 16 × AB

AB = 16 / 2√3

AB = 8 / √3

So , Height of the tree = AC + AB

=> 16 / √3 + 8 / √3

=> 24 / √3

Multiplying √3 in numerator and denominator ...

=> 24 / √3 × √3 / √3

=> 24 × √3 / 3

=> 8√3

Height of the tree is 8√3 m