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MHT CET202521 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , with usual notations if a=4, ~b =8, C =60^ , then the value of B and the ratio A : C respectively are,

Options

  1. A4 ,~ 1: 3
  2. B2 ,~ 3 : 1
  3. C2 ,~ 2: 3
  4. D6 ,~ 3 : 2

Correct answer

B. 2 ,~ 3 : 1

Step-by-step solution

Given triangle sides a = 4 , b = 8 , and included angle C = 60^ , determine angle B and the ratio A : C . Using the Law of Cosines, side c is found by: c^2 = a^2 + b^2 - 2ab C = 4^2 + 8^2 - 2 4 8 60^ = 16 + 64 - 64 1 2 = 48 Thus, c = 48 = 4 3 . To find angle B, apply the Law of Sines: b B = c C 8 B = 4 3 60^ = 4 3 3 /2 = 8 So B = 1 and B = 90^ = 2 . A = 180^ - 90^ - 60^ = 30^ Now compute the cosine ratio: A = 30^ = 3 2 C = 60^ = 1 2 The ratio simplifies to 3 2 : 1 2 = 3 : 1 So B = 2 and A : C = 3 : 1 , matching opt

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