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MHT CET202620 April 2026Evening ShiftMathematicsProperties of TrianglesActual

With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

Options

  1. A2
  2. B3
  3. C2 3
  4. D4

Correct answer

C. 2 3

Step-by-step solution

Let the sides of the triangle be a = 3 , b = 5 , and c = 7 . The largest angle of a triangle is opposite to its longest side. Thus, the largest angle is C , which is opposite to the side c = 7 . Using the cosine rule: C = a^2 + b^2 - c^2 2ab Substituting the given values: C = 3^2 + 5^2 - 7^2 2(3)(5) C = 9 + 25 - 49 30 C = 34 - 49 30 C = -15 30 = - 1 2 Since 0 < C < , we get C = 2 3 .

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