Multiple choice

The upper part of a tree broken over by the wind makes an angle of $30^{o}$ with the ground, and the distance from the root to the point where the top of the tree meets the ground is $15\ m$. The present height of the tree is

  1. $15\ m$
  2. $10\sqrt{3}\ m$
  3. $20\ m$
  4. $None\ of\ these$
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D Correct answer
AI explanation

Let the unbroken part be x and the broken part be y; using trigonometric ratios, tan(30 degrees) equals x divided by 15, making x equal to 15 divided by the square root of 3. Also, cos(30 degrees) equals 15 divided by y, so y equals 15 multiplied by the square root of 3 divided by 3, which is 5 multiplied by the square root of 3. The present height of the broken tree is x plus y, which is 15 divided by the square root of 3 plus 5 multiplied by the square root of 3, yielding 10 multiplied by the square root of 3 m. As this exact value is not listed among the options, the correct choice is None of these.

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