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AP EAMCET202124 Aug 2021Morning ShiftMathematicsProperties of TrianglesActual

In A B C, a=6 ~cm , b=10 ~cm and c=14 ~cm . Then, the sum of the acute angles of the triangle is

Options

  1. A180^
  2. B120^
  3. C90^
  4. D60^

Correct answer

D. 60^

Step-by-step solution

For A B C aligned a & =6 ~cm , b=10 ~cm and c=14 ~cm A & = b^2+c^2-a^2 2 b c & = 10^2+14^2-6^2 2 10 14 = 100+196-36 2 10 14 & = 296-36 2 10 14 = 260 2 10 14 A & = 13 14 aligned A is acute angle. aligned B & = a^2+c^2-b^2 2 a c & = 6^2+14^2-10^2 2 6 14 = 36+196-100 2 6 14 & = 132 2 6 14 B & = 11 14 aligned B is acute angle. aligned & C= a^2+b^2-c^2 2 a b = 6^2+10^2-14^2 2 6 10 = 136-196 2 6 10 & = -60 2 6 10 =- 1 2 & C=- 1 2 & C=120^ & Sum of acute angle =A+B=180-C & =180-120=60^ & aligned

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