a) Áp dụng định lí côsin: $AB^2=AC^2+BC^2-2 \cdot AC \cdot BC \cdot cosC$
$\Rightarrow AB^2=15^2+12^2-2 \cdot 15 \cdot 12 \cdot cos120^{\circ}$
$\Rightarrow AB=\sqrt{15^2+12^2-2 \cdot 15 \cdot 12 \cdot cos120^{\circ}}$
$\Rightarrow AB \approx 23,4$.
b) Áp dụng định lí sin: $\frac{AB}{sinC}=\frac{AC}{sinB}=\frac{BC}{sinA}$
$\Rightarrow \frac{23,4}{sin120^{\circ}}=\frac{15}{sinB}=\frac{12}{sinA}$
$\Rightarrow sinB \approx 0,56 \Rightarrow \widehat{B} = 34^{\circ}$
$\Rightarrow \widehat{A} = 26^{\circ}$
c) $S=\frac{1}{2} \cdot BC \cdot AC \cdot sinC=\frac{1}{2} \cdot 12 \cdot 15 \cdot sin120^{\circ}=45\sqrt{3}$