Question

the upper part of tree , broken by wind makes angel of 30 with the ground. too of tree touches ground at a distance of 5 m.the original height of tree is
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Answer 1

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Answer 2

Refer to the attachment.

Given :-

▪ The upper part of tree is broken by wind makes angle of θ = 30° with the ground.

▪ The top of the tree touches the ground at a distance of 5 m .

To Find :-

▪ Original height of the tree.

Solution :-

As given in the diagram, imagine the given situation in a right angled triangle, where the hypotenuse is the broken part , base be the distance from the tree of the top of tree and perpendicular be the unbroken part.

It is clear that,

⇒ Original height = Broken part + Unbroken part

⇒ h = BC + AC ...(1)

Let us find BC and AC first

In the ∆ABC,

⇒ tan θ = Perpendicular / Base

⇒ tan 30° = BC / AB

⇒ 1/√3 = BC / 5

⇒ BC = 5 / √3 m ...(2)

Also,

In ∆ABC,

⇒ cos θ = Base / Hypotenuse

⇒ cos 30° = AB / AC

⇒ 1 / 2 = 5 / AC

⇒ AC = 10 m ...(3)

Substituting values of BC and AC in (1),

⇒ Original height = BC + AC

⇒ Original height = 5/√3 + 10

⇒ Original height = (5 + 10√3) / √3

⇒ Original height = (5√3 + 30) / 3

Substituting √3 = 1.73

⇒ Original height = (5×1.73 + 30) / 3

⇒ Original height = 38.65 / 3

⇒ Original height = 12.88 m

Hence, The original height of the tree is 12.88 m