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AP EAMCET202018 Sep 2020Morning ShiftMathematicsProperties of TrianglesActual

In a ( A B C, C=60^ ) and ( A=75^ ). If (D ) is a point on (A C ) such that the area of ( B A D ) is ( 3 ) times the area of ( B C D ), then the measure of ( A B D ) is

Options

  1. A(30^ )
  2. B(45^ )
  3. C(60^ )
  4. D(90^ )

Correct answer

A. (30^ )

Step-by-step solution

In a ( A B C ), it is given the angles (A=75^ ) and (C=60^ ) and ( B A D= 3 ( B C D) (A D)= 3 (C D) ) ( A D C D = 3 ) As angle (B=45^ ), Now let ( A B D= ), then ( D B C=45^ - ) Now, by sine law ( gathered A D = 75^ B D ,( in A B D) and (45^ - ) C D = 60^ B D ,( in D B C) (C D) (A D) (45^ - ) = 75^ 60^ 1 3 (45^ - ) = 1 2 2 + 3 2 2 3 2 (45^ - ) = 3 +1 2 (45^ - ) = 3 -1 2 1 2 - 1 2 = 3 -1 2 = 3 =30^ gathered )

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