Question

A tree bent by the wind .The top of the tree meets the ground at an angle of 60.If the distance between the top of the foot be 8 m then what was the height of the tree?

Answer 1

Step-by-step explanation:

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Answer 2

The height of the tree will be 16+8√3 m.

Given,

The tree is bent by the wind and meets the ground at an angle of 60°.

The distance between the top to the foot of the tree is 8m.

To Find,

The height of the tree.

Solution,

The bent tree forms an right angles triangle with the ground, with the base as 8m.

Now,

tan θ = Perpendicular/Base

So,

tan 60 = Perpendicular/8

Perpendicular = 8√3 m.

Now,

sin θ = Perpendicular/Hypotenuse

sin 60 = 8√3/hypotenuse

hypotenuse = 8√3/(√3/2) = 16 m.

Now, the height of the tree will be base + hypotenuse

So, the height of the tree = 16+8√3 m

Hence, the height of the tree will be 16+8√3 m.

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