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A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75^ . What is the height of the flagstaff?

Options

  1. A12 m
  2. B9 m
  3. C(6+ 3 ) m
  4. D(6+3 3 ) m

Correct answer

D. (6+3 3 ) m

Step-by-step solution

Let A C is a flagstaff of length h ~m and B D is a ladder of length 6 m . Point B is below the top of the flagstaff, such that A B=6 ~m . Then, A D C=75^ . aligned & From A C D, C A D+ A D C+ A C D=180^ & C A D+75^ +90^ =180^ & C A D=180^ -90^ -75^ =15^ aligned aligned & As, A B=B D . & C A D= B D A=15^ and & B D C=75^ -15^ =60^ . aligned aligned & From B C D, (60^ )= B C B D = B C 6 & B C=6 (60^ )=6 3 2 =3 3 aligned Hence, height of flagstaff =(6+3 3 ) m .

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