Multiple choice

A tree $10(2+\sqrt 3)$ metres high is broken by the wind at a height $10\sqrt 3$ metres from its root in such a way that top struck the ground at certain angle and horizontal distance from the root of the tree to the point where the top meets the ground is $10m$. Find the angle of elevation made by top of the tree with the ground.

  1. ${80}^{o}$
  2. ${60}^{o}$
  3. ${40}^{o}$
  4. ${20}^{o}$
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B Correct answer
Explanation

The broken portion has length 10(2 + √3) - 10√3 = 20 m. It forms a right triangle with horizontal side 10 m and vertical side 10√3 m, so tan θ = √3 and θ = 60°.

AI explanation

The vertical distance from the break point to the ground is 10 times the square root of 3 meters. Using the definition of the tangent ratio for the angle of elevation, we have tan(theta) equals the vertical height divided by the horizontal distance of 10 meters. This gives tan(theta) equals the square root of 3, so the angle of elevation is 60 degrees.

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