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AP EAMCET202022 Sep 2020Evening ShiftMathematicsSequences and SeriesActual

The angles A, B, C of a triangle A B C are in AP. If A B=6, B C=7 , then A C=

Options

  1. A40
  2. B41
  3. C43
  4. D6

Correct answer

C. 43

Step-by-step solution

aligned & (c) Given In A B C , & A, B, C are in AP & & In A B C, aligned aligned A+ B+ C & =180^ 2 B+ B & =180^ B & =60^ aligned From cosine rule, aligned B & = A B^2+B C^2-A C^2 2 A B B C 60^ & = 36+49-x^2 2 6 7 1 2 & = 85-x^2 84 41 & =85-x^2 aligned aligned x^2 & =85-42 x^2 & =43 x & = 43 aligned Hence, option (3) is correct.

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