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In a Δ A B C , a b = 2 + 3 , and ∠ C = 60 ° . Then the ordered pair ( ∠ A , ∠ B ) is equal to:

Options

  1. A105 ° ,   15 °
  2. B15 ° ,   105 °
  3. C45 ° ,   75 °
  4. D( 75 ° ,   45 ° )

Correct answer

A. 105 ° ,   15 °

Step-by-step solution

a b > 1 ⇒ ∠ A > ∠ B A + B = 120 ° ⇒ s i n ( 120 ° − B ) s i n B = 2 + 3 ⇒   3 2 c o t B + 1 2 = 2 + 3 ⇒   c o t B = 2 3 3 2 + 3   ⇒ c o t B = 2 + 3 ⇒     B = 15 ° Hence, ( ∠ A , ∠ B ) = ( 105 ° , 15 ° )

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