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AP EAMCET20224 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

In a triangle A B C , a b = 2 + 3 and ∠ C = 60 ° . Then the measure of ∠ A is

Options

  1. A95 °
  2. B65 °
  3. C105 °
  4. D115 °

Correct answer

C. 105 °

Step-by-step solution

Given: a b = 2 + 3 ∠ C = 60 ° Also, A + B + C = 180 ° ⇒ A + B = 120 °           . . . 1 By sine formula sin A a = sin B b ⇒ sin A sin B = a b ⇒ sin A sin B = 2 + 3 Applying Componendo and Dividendo, we get sin A + sin B sin A - sin B = 3 + 3 3 + 1 ⇒ 2 sin A + B 2 cos A - B 2 2 sin A - B 2 cos A + B 2 = 3 + 3 3 + 1 ⇒ sin 60 ° cos A - B 2 sin A - B 2 cos 60 ° = 3 1 + 3 3 + 1 ⇒ 3 cot A - B 2 = 3 ⇒ cot A - B 2 = 1 ⇒

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