Multiple choice

A tree breaks due to storm and the broken part bends so that the top of the three touches the ground making an angle $30^0$ 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.

  1. $\dfrac{12}{\sqrt3}$
  2. ${24}{\sqrt3}$
  3. $\dfrac{8}{\sqrt3}$
  4. ${8}{\sqrt3}$
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D Correct answer
Explanation

The broken portion forms a right triangle with horizontal distance 8 m and angle 30 degrees at the ground. The standing portion is 8/sqrt(3) m, and the broken portion is 16/sqrt(3) m. Their sum is 24/sqrt(3) = 8sqrt(3) m.

AI explanation

The unbroken part of the tree forms a 30 degree angle with the ground, and using the tangent ratio gives the vertical height as 8 tan(30 degrees), which is 8 divided by the square root of 3. The broken part serves as the hypotenuse, calculated using the cosine ratio as 8 sec(30 degrees), equaling 16 divided by the square root of 3. Adding these two lengths gives the total height of the tree as 24 divided by the square root of 3, which rationalizes to 8 times the square root of 3.

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