Verified Solution • 2025–26 Session moderate

QJEEM19Macfa5: JEE Main 2019 Mathematics - Class 11 JEEM19Macfa5 Solution: Given for a ABC with usual notation. If    then the…

Given b+c11=c+a12=a+b13{{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}} for a Δ\Delta ABC with usual notation.

If    cos⁡Aα=cos⁡Bβ=cos⁡Cγ,{{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma }, then the ordered triad ( α\alpha , β\beta , γ\gamma ) has a value :

Multiple Choice Options

  • A (19, 7, 25)
  • B (7, 19, 25)
  • C (5, 12, 13)
  • D (3, 4, 5)

Step-by-Step Verified Solution

b + c = 11 λ\lambda , c + a = 12 λ\lambda , a + b = 13 λ\lambda

⇒\Rightarrow   a = 7 λ\lambda , b = 6 λ\lambda , c = 5 λ\lambda

(using cosine formula)

cosA = 15,{1 \over 5}, cosB = 1935,{19 \over 35}, cosC = 57,{5 \over 7},

α\alpha : β\beta : γ\gamma ⇒\Rightarrow   7 : 19 : 25

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