Multiple choice

At a distance $2h$ $m$ from the foot of a tower of height $h$ $m$, the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

  1. $\dfrac { 5h }{ 3 } m$
  2. $\dfrac { 4h }{ 3 } m$
  3. $\dfrac { 7h }{ 5 } m$
  4. $\dfrac { 3h }{ 2 } m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the pole height be x. The tower height is h. Angle at distance 2h is tan(theta) = h / 2h = 0.5. The pole is at the top, so the total height is h + x. The angle subtended by the pole is the difference between the angle to the top of the pole and the angle to the top of the tower. Setting these equal leads to the result x = 5h/3.

Keep practicing — related questions