Multiple choice

A flagstaff $5$ m high is placed on a building $25$ m high. If the flag and building be subtend equal angels on the observer at a height $30$ m, then the distance between observer and the top of flag is

  1. $\dfrac {5\sqrt {3}}{2}$
  2. $5\sqrt {\dfrac {2}{3}}$
  3. $5\sqrt {\dfrac {3}{2}}$
  4. $\dfrac {5\sqrt {2}}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the observer be at (0, 30). The building top is at (x, 25) and flag top is at (x, 30). The angles subtended are equal, implying the ratio of heights to horizontal distance is the same. Solving the geometry leads to the distance between the observer and the flag top.

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