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Q.

A tree 12 m high is broken by the wind in such a way that its top touches the ground and makes an angle 60∘with the ground. At what height from the bottom the tree is broken by the wind?


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a

5.569 m

b

1.732 m

c

5.59 m

d

2.456 m  

answer is A.

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Detailed Solution

Given,
Question ImageHeight of the tree = AC+BC=12 m,
Considering AC=x m,
We have the formula,
tanθ=heightbase We have to find the height from the bottom,
In ΔABC,
 sin60∘=x12-x ⇒ 32=x12-x ⇒ 3(12-x)=2x ⇒123-3x=2x ⇒123=2x+3x ⇒123=x(2+3) ⇒ x=1232+3 ⇒ x=(123)(2-3)(2+3)(2-3)  ⇒x=(123)(2-3)4-3 ⇒ x=123(2)-12×3 ⇒ x=243-36 ⇒x=5.569 m   (Taking 3=1.732)
Thus, the value of x is 5.569m.
Therefore the correct option is 1.
 
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