Question

a tree broken by the wind. the top touched the ground making angle of30°and at adistance of 30m from the foot of the tree. what was the height of the tree?(root 3 =1.73)

Answer 1

Given that:

distance between the foot of the tree and the broken part of the tree that touches the ground=30m

so , let ,

the height of standing part of the tree be = h

the height of fallen part (forms hypotenuse) be = x

then the total height of the tree will be = h + x

now,

tan 30 = h/30 m

1/√3 = h/30 m

30/√3 = h

⇒ h= 30/√3 m ..... 1

similarly,

cos 30 = 30 m/ x

√3/2 = 30 / x

√3x = (30)2

√3x = 60 m

⇒ x = 60 / √3 m ......2

( we now have both value of h and x )

on adding equation1 & 2 :

⇒ h + x = 30 /√3 +60 /√3

=90 /√3 m

= 60√3 m

Hence, the total height of the tree is 60√3 m .

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I hope it will helps you friend ^-^