Multiple choice

Two men standing on opposite sides of a flag staff measure the angles of the top of the flagstaff as $30^{\circ}$ and$\, 60^{\circ}$. If the height of the flagstaff is $18$ m the distance between the men is :

  1. $24$ m
  2. $\displaystyle24\sqrt{3}m$
  3. $\displaystyle\frac{24}{\sqrt{3}}m$
  4. $31.2$ m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let h be the height (18m) and d be the distance. The distance is h * (cot 30 + cot 60). This is 18 * (sqrt(3) + 1/sqrt(3)) = 18 * (3/sqrt(3) + 1/sqrt(3)) = 18 * (4/sqrt(3)) = 72/sqrt(3) = 24 * sqrt(3).

AI explanation

The two men and the base of the flagstaff form two right triangles with a common height of 18 m. Using the tangent ratio, the distance from the first man to the base is 18 divided by tan(60 degrees), which equals 18 divided by the square root of 3, or 6 times the square root of 3 m. The distance from the second man is 18 divided by tan(30 degrees), which equals 18 times the square root of 3 m. Adding these two distances gives a total distance of 24 times the square root of 3 m.

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