.

Biết:

\(B = 60^{\circ} , A B = 3 , B C = 4 , 5.\)

Dùng định luật cos:

\(A C^{2} = A B^{2} + B C^{2} - 2 \left(\right. A B \left.\right) \left(\right. B C \left.\right) cos ⁡ 60^{\circ}\)

\(A C^{2} = 3^{2} + 4 , 5^{2} - 2 \cdot 3 \cdot 4 , 5 \cdot \frac{1}{2} = 15 , 75.\)

\(A C \approx 3 , 97 \&\text{nbsp};\text{cm} .\)

Dùng định luật cos tiếp:

\(A \approx 79 , 1^{\circ} .\)

Do đó:

\(C = 180^{\circ} - 60^{\circ} - 79 , 1^{\circ} \approx 40 , 9^{\circ} .\)

Đáp án:
\(\boxed{A C \approx 3 , 97 \&\text{nbsp};\text{cm} , A \approx 79 , 1^{\circ} , C \approx 40 , 9^{\circ}}\)

Biết:

\(B = 70^{\circ} , A B = 2 , 1 , A C = 3 , 8.\)

Theo định luật sin:

\(\frac{sin ⁡ B}{A C} = \frac{sin ⁡ C}{A B}\)

nên

\(sin ⁡ C = \frac{2 , 1 sin ⁡ 70^{\circ}}{3 , 8} \approx 0 , 518.\)

Suy ra:

\(C \approx 31 , 2^{\circ} .\)

Vậy:

\(A = 180^{\circ} - 70^{\circ} - 31 , 2^{\circ} \approx 78 , 8^{\circ} .\)

Tiếp tục:

\(\frac{B C}{sin ⁡ A} = \frac{A C}{sin ⁡ B}\)

\(B C = \frac{3 , 8 sin ⁡ 78 , 8^{\circ}}{sin ⁡ 70^{\circ}} \approx 3 , 99 \&\text{nbsp};\text{cm} .\)

Đáp án:
\(\boxed{C \approx 31 , 2^{\circ} , A \approx 78 , 8^{\circ} , B C \approx 3 , 99 \&\text{nbsp};\text{cm}}\)

1. \(A = 180^{\circ} - 65^{\circ} - 40^{\circ} = 75^{\circ} .\)

   Với \(B C = 4 , 2\) cm:

   \(\frac{B C}{sin ⁡ 75^{\circ}} = \frac{A C}{sin ⁡ 65^{\circ}} = \frac{A B}{sin ⁡ 40^{\circ}} .\)

   Do đó:

   \(A C = \frac{4 , 2 sin ⁡ 65^{\circ}}{sin ⁡ 75^{\circ}} \approx 3 , 94 \&\text{nbsp};\text{cm}\)

   \(A B = \frac{4 , 2 sin ⁡ 40^{\circ}}{sin ⁡ 75^{\circ}} \approx 2 , 80 \&\text{nbsp};\text{cm} .\)

   Đáp án:
   \(\boxed{A = 75^{\circ} , \&\text{nbsp}; A C \approx 3 , 94 \&\text{nbsp};\text{cm} , \&\text{nbsp}; A B \approx 2 , 80 \&\text{nbsp};\text{cm}}\)

   
   

1. \(A = 180^{\circ} - 65^{\circ} - 45^{\circ} = 70^{\circ} .\)

   Vì \(A B = 2 , 8\) cm, theo định luật sin:

   \(\frac{A B}{sin ⁡ 45^{\circ}} = \frac{B C}{sin ⁡ 70^{\circ}} = \frac{A C}{sin ⁡ 65^{\circ}} .\)

   Suy ra:

   \(B C = \frac{2 , 8 sin ⁡ 70^{\circ}}{sin ⁡ 45^{\circ}} \approx 3 , 72 \&\text{nbsp};\text{cm}\)

   \(A C = \frac{2 , 8 sin ⁡ 65^{\circ}}{sin ⁡ 45^{\circ}} \approx 3 , 59 \&\text{nbsp};\text{cm} .\)

   Đáp án:
   \(\boxed{A = 70^{\circ} , \&\text{nbsp}; B C \approx 3 , 72 \&\text{nbsp};\text{cm} , \&\text{nbsp}; A C \approx 3 , 59 \&\text{nbsp};\text{cm}}\)