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MHT CET202523 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle A B C , with usual notations, if a=5, b=4, (A-B)= 31 32 , then c=

Options

  1. A6
  2. B7
  3. C5
  4. D2

Correct answer

A. 6

Step-by-step solution

Given: In a triangle, sides a = 5 , b = 4 , and (A - B) = 31 32 . Find side c . Using the identity (A - B) = A B + A B , express the trigonometric functions in terms of the sides via the cosine rule: A = b^2 + c^2 - a^2 2bc = 16 + c^2 - 25 8c = c^2 - 9 8c B = a^2 + c^2 - b^2 2ac = 25 + c^2 - 16 10c = c^2 + 9 10c Using the sine rule, A = a C c = 5 C c and B = b C c = 4 C c . Substitute into the identity: 31 32 = ( c^2 - 9 8c ) ( c^2 + 9 10c ) + ( 5 C c ) ( 4 C c ) = c^4 - 81 80c^2 + 20 ^2 C c^2 Now express ^2 C in t

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