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AP EAMCET202119 Aug 2021Morning ShiftMathematicsProperties of TrianglesActual

In ∆ A B C , A = 75 ° , B = 45 ° then the value of b + c 2 =

Options

  1. Aa
  2. B3 a
  3. C2 a
  4. D4 a

Correct answer

C. 2 a

Step-by-step solution

Given in ∆ A B C ,   A = 75 ° , B = 45 ° ⇒ C = 180 ° - 75 ° - 45 ° = 60 ° (Using Angle Sum property of triangle) Also, sin 75 ° = 3 + 1 2 2 , sin 45 ° = 1 2 and sin 60 ° = 3 2 Now, using Sine rule, a sin A = b sin B = c sin C ⇒ a 3 + 1 2 2 = b 1 2 = c 3 2 ⇒ 2 2 a 3 + 1 = 2 b = 2 c 3 ⇒ b = 2 2 a 2 3 + 1 = 2 a 3 + 1 and c = 2 2 a 3 + 1 × 3 2 = 6 a 3 + 1 Now, L . H . S . = b + c 2 = 2 a 3 + 1 + 6 a 3 + 1 × 2 = 2 a + 2 3 a 3 + 1 =

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