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MHT CET202611 April 2026Evening ShiftMathematicsProperties of TrianglesActual

In triangle ABC, with usual notations, if the angles are in Arithmetic Progression and 3c^2 = 2b^2 , then the measure of angle A is

Options

  1. A5 12
  2. B7 12
  3. C5 6
  4. D7 6

Correct answer

A. 5 12

Step-by-step solution

Given that the angles A, B, C of the triangle are in Arithmetic Progression. 2B = A + C Since A + B + C = , we have: 3B = B = 3 We are given the relation 3c^2 = 2b^2 . Using the Sine Rule, b = 2R B and c = 2R C , we can substitute these into the given relation: 3(2R C)^2 = 2(2R B)^2 3 ^2 C = 2 ^2 B Substituting B = 3 and B = 3 2 : 3 ^2 C = 2 ( 3 2 )^2 3 ^2 C = 2 3 4 = 3 2 ^2 C = 1 2 C = 1 2 (since C > 0 for angles in a triangle) This gives C = 4 or C = 3 4 . If C = 3 4 , then B + C = 3 + 3 4 = 13 12 > , which is no

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