Multiple choice

The angle of elevation of a tower from a distance $100\ m$ from its foot is ${30}^{o}$. Height of the tower is:

  1. $100\sqrt {3\ m}$
  2. $\dfrac {100}{\sqrt {3}}m$
  3. $50\sqrt {3\ m}$
  4. $\dfrac {200}{\sqrt {3}}m$
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B Correct answer
Explanation

In the right triangle, tan(30°) = height/100. Since tan(30°) = 1/sqrt(3), the height is 100/sqrt(3) m.

AI explanation

We use the basic trigonometric ratio for the tangent of an angle of elevation, which is the height of the tower divided by its horizontal distance from the foot. Given the distance is 100 m and the angle of elevation is 30 degrees, we write tan(30 degrees) = Height / 100. The value of tan(30 degrees) is 1 divided by the square root of 3, so the equation becomes 1 divided by the square root of 3 = Height / 100. Multiplying both sides by 100 gives the height of the tower as 100 divided by the square root of 3 meters.

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