Question

A tree is broken by the wind. the top of the tree stuck the ground an angle of 30degree and the distance of 30degree in from the root. find the height of the whole tree. (√3 = 1.73)
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Answer 1

Solution :-- seg AB represents the height of the tree

The tree breaks at point D

∴ seg AD is the broken part of tree which then takes the position of DC

∴ AD = DC

m∠ DCB = 30º

BC = 30 m

In right angled ∆DBC,

tan 30º = side opposite to angle 30º/adjacent side of 30º

∴ tan 30º = BD/BC

∴ 1/√3 = BD/30

∴ BD = 30/√3

∴ BD = (30/√3)×(√3/√3)

∴ BD = 10√3 m

cos 300 = adjacent side of angle 300/Hypotenuse

∴ cos 300 = BC/DC

∴ cos 300 = 30/DC

∴ √3/2 = 30/DC

∴ DC = (30×2)/√3

∴ DC = (60/√3)×(√3/√3)

∴ DC = 20√3 m

AD = DC = 20 √3 m

AB = AD + DB [∵ A - D - B]

∴ AB = 20 3 + 10 3

∴ AB = 30 3 m

∴ AB = 30 × 1.73

∴ AB = 51.9 m

∴ The height of tree is 51.9 m.