Multiple choice

The angles of elevation of the top and foot of a flag staff fixed on a wall are $60^o$ and $45^o$ to a man, standing on the other end, at a distance of $30$m. Find the height of the flag staff.

  1. $30\sqrt 3$
  2. $30(\sqrt 3-1)$m
  3. $30(\sqrt 3+1)$m
  4. $10\sqrt 3$m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let wall height be h, flag staff height be f, distance 30m. tan(45) = h/30 => h = 30. tan(60) = (h+f)/30 => sqrt(3) = (30+f)/30 => 30*sqrt(3) = 30+f => f = 30(sqrt(3)-1).

AI explanation

Using the tangent ratio for the angle to the wall, tan(45 degrees) = height of wall / 30, meaning the wall's height is 30 m. For the angle to the top of the flag staff, tan(60 degrees) = (wall height + flag staff height) / 30, which sets sqrt(3) = (30 + flag staff height) / 30. Solving this gives the total height as 30*sqrt(3) m, so the height of the flag staff is 30*sqrt(3) minus 30, resulting in 30*(sqrt(3) - 1) m.

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