Multiple choice

The angle of elevation of the top of an unfinished tower from a point at a distance of $120$ metres from its base is $45^{0}$. The height of the tower that must be raised so that the angle of elevation at the same point will be $60^{0}$ is

  1. $120(\sqrt{3}-1)m$
  2. $120(\sqrt{3}+1)m$
  3. 120 $\sqrt{3}m$
  4. 140 $\sqrt{3}m$
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A Correct answer
Explanation

Initial height h1 = 120 * tan(45) = 120. Final height h2 = 120 * tan(60) = 120 * sqrt(3). Height to be raised = 120 * sqrt(3) - 120 = 120(sqrt(3) - 1).

AI explanation

The initial height of the unfinished tower is found using the tangent of the 45 degree angle of elevation, giving a height of 120 meters since tan 45 degrees is 1. When the angle of elevation becomes 60 degrees, the total new height of the tower is 120 times tan 60 degrees, which equals 120 times the square root of 3 meters. The required increase in height is the difference between the new height and the old height, calculated as 120 times the square root of 3 minus 120, which factors to 120 times (the square root of 3 minus 1) meters.

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