JEE Main20246 Apr 2024Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , BC =7, AC =8, AB = N and A = 2 3 . If 49 (3 C )+42= m n , where gcd ( m , n )=1 , then m + n is equal to________

Correct answer

Step-by-step solution

aligned & A = b ^2+ c ^2- a ^2 2 bc & 2 3 = 8^2+ c ^2-7^2 2 8 c & C =9 & C = 7^2+8^2-9^2 2 7 8 = 2 7 & 49 3 C +42 & 49 (4 ^3 C -3 C )+42 & 49 (4 ( 2 7 )^3-3 ( 2 7 ) )+42 & = 32 7 & ~m + n =32+7=39 aligned

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