A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. 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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This answer was edited.In right ΔABD,

Using Cosine ratio,

cos 30° = AD/BD

We know that, cos 30° = √3/2

√3/2 = 8/BD

∴AC = 16/√3 …(1)

using tangent ratio,

tan 30° = AB/AD

1/√3 = AB/8

AB = 8/√3 ….(2)

Total height of the tree is the sum of AB and BC,

Therefore, total height of the tree = AB + BC

16/3+ 8/√3 = 24/√3 = 8√3 m.