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A tree breaks due to a 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. The height of the tree was

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73 m

53 m

83 m

23 m

answer is C.

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Detailed Solution

Given that,
Distance between foot of tree and top of tree touching ground = 8 m,
Height of the broken part of the tree in air above the ground = AB and,
Angle made by the broken tree touches the ground,

θ = 30 °

.
The situation represented diagrammatically is as follows,
Question Image

For the broken part of the tree,
Question Image

⇒ cos 30 ° = 8 A C ⇒ 32 = 8 A C ⇒ A C = 8 × 2 3 ⇒ A C = 163

Original length of tree = AB +AC
=

83 + 163 = 243

= 83 m

Therefore, the original height if the tree was

83 m .

The correct option is 3.

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