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in Trigonometry by (56.3k points)

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

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Best answer

Let the initial height of the tree be AC.

And, due to storm the tree is broken at B.

Let the bent portion of the tree be AB = x m and the remaining portion BC = h m

So, the height of the tree AC = (x + h) m

And, given DC = 8m

Now, in ΔBCD

tan 30o = BC/DC

1/√3 = h/8

h = 8/√3

Next, in ΔBCD

cos 30o = DC/BD

√3/2 = 8/x

x = 16/√3 m

So, x + h = 16/√3 + 8/√3

= 24/√3 = 8√3

Therefore, the height of the tree is 8√3 m.

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