Multiple choice

The angle of elevation of the top of a tower at a distance 500 meters from the foot is $30^0$. The height of the tower is

  1. $250\sqrt 3$ meters
  2. $\dfrac{500}{\sqrt3} $ meters
  3. $500\sqrt 3 $ meters
  4. $250$ meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The height of the tower h is related to the distance d by tan(30) = h/d. Thus, h = 500 * tan(30) = 500 * (1/sqrt(3)) = 500/sqrt(3).

AI explanation

Using the trigonometric ratio for the right triangle formed by the tower and the ground, tan(30) equals the height of the tower divided by the distance of 500 meters. Since the value of tan(30) is 1 divided by the square root of 3, the height is 500 divided by the square root of 3 meters.

Keep practicing — related questions