Multiple choice

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of $100\ m$ from its base is $\displaystyle 45^{o}$ If the angle of elevation of the top of the complete pillar at the same point is to be $\displaystyle 60^{o}$ then the height of the incomplete pillar is to be increased by

  1. $\displaystyle 50\sqrt{2}\ m$
  2. $100\ m$
  3. $\displaystyle 100\left ( \sqrt{3-1} \right )\ m$
  4. $\displaystyle 100\left ( \sqrt{3+1} \right )\ m$
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C Correct answer
AI explanation

At a horizontal distance of 100 m, the initial height of the pillar is found using tan 45 degrees equals h1 over 100, making h1 equal to 100 m. The completed height h2 is found using tan 60 degrees equals h2 over 100, so h2 equals 100 times the square root of 3. The required increase in height is the difference h2 minus h1, which is 100 multiplied by the square root of 3 minus 1 m.

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