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MHT CET202616 April 2026Evening ShiftMathematicsProperties of TrianglesActual

In triangle ABC, with usual notations, if a = 4, b = 5 and c = 6 , then angle C is equal to...

Options

  1. AA
  2. B2A
  3. C3A
  4. DA 2

Correct answer

B. 2A

Step-by-step solution

Using the cosine rule: A = b^2 + c^2 - a^2 2bc A = 5^2 + 6^2 - 4^2 2(5)(6) = 25 + 36 - 16 60 = 45 60 = 3 4 Similarly, for angle C: C = a^2 + b^2 - c^2 2ab C = 4^2 + 5^2 - 6^2 2(4)(5) = 16 + 25 - 36 40 = 5 40 = 1 8 Using the double angle formula: 2A = 2 ^2 A - 1 2A = 2 ( 3 4 )^2 - 1 = 2 ( 9 16 ) - 1 = 9 8 - 1 = 1 8 Since C = 2A and both angles lie in (0, ) , we get C = 2A . Answer: 2A

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