Multiple choice

$A$ man observes a tower$AB$ of height $h$ from a point $P$ on the ground. He moves a distance d' towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance $\dfrac {3d}{4}$ in the same direction and the angle of elevation is three times that at $P$. Then $\displaystyle \frac{h^{2}}{d^{2}}=$

  1. $\dfrac {35}{9}$
  2. $\dfrac {35}{36}$
  3. $\dfrac {36}{5}$
  4. $\dfrac {36}{35}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the initial angle be theta and the initial horizontal distance be x. Using tan(2theta) and tan(3theta) with the two stated movements gives tan^2(theta) = 5/7 and d/x = 6/7. Hence h^2/d^2 = tan^2(theta)/(d/x)^2 = 35/36.

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