Multiple choice

The angle of elevation of the top of a tower from the top of a house is ${ 60 }^{ o }$ and the angle of depression of its base is ${ 30 }^{ o }$. If the horizontal distance between the house and the tower be $12 m$, then the height of the tower is

  1. $48\sqrt { 3 } m$
  2. $16\sqrt { 3 } m$
  3. $24\sqrt { 3 } m$
  4. $\dfrac { 16 }{ \sqrt { 3 } } m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let h be the height of the house. Height of tower = h + x. tan(60) = x / 12, so x = 12 * sqrt(3). tan(30) = h / 12, so h = 12 / sqrt(3) = 4 * sqrt(3). Total height = 12 * sqrt(3) + 4 * sqrt(3) = 16 * sqrt(3).

AI explanation

The horizontal distance between the house and the tower is 12 m. Using the 30 degree angle of depression, the height of the house is calculated as 12 tan 30, which equals 12 / sqrt(3) m. The height of the tower above the house is found using the 60 degree angle of elevation, giving 12 tan 60, which is 12 sqrt(3) m. The total height of the tower is the sum of these two heights, 12 / sqrt(3) + 12 sqrt(3), which simplifies to 16 sqrt(3) m.

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