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

Question

In a Δ A B C , a b = 2 + 3 , and ∠ C = 60 ° . Then the ordered pair ( ∠ A , ∠ B ) is equal to:, 105 ° , 15 °, 15 ° , 105 °, 45 ° , 75 °, ( 75 ° , 45 ° )

MARKS App · Accepted Answer

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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