a) Áp dụng định lí côsin, ta có:
a = $\sqrt{b^{2} + c^{2} - 2bc.cosA}$
= $\sqrt{8^{2} + 5^{2} - 2. 8. 5. cos120^{\circ}} \approx$ 11,4
Áp dụng định lí sin, ta có: $\frac{a}{sinA}$ = $\frac{b}{sinB}$
$\Rightarrow sinB = \frac{bsinA}{a} = \frac{8.sin120^{\circ}}{11,4} \approx$ 0,61
$\Rightarrow \widehat{B} = 37^{\circ}35'$
$\Rightarrow \widehat{C} = 180^{\circ} - 37^{\circ}35' - 120^{\circ} = 22^{\circ}25'$
b) S = $\frac{1}{2}bcsinA$ = $\frac{1}{2}.8.5.sin120^{\circ}$ = $10\sqrt{3}$
c) Áp dụng định lí sin, ta có: $\frac{a}{sinA}$ = 2R
$\Rightarrow$ R = $\frac{a}{2sinA} = \frac{11,4}{2.sin120^{\circ}}$ = 6,6
Ta có: S = $\frac{1}{2}$.AH. BC $\Rightarrow$ AH = $\frac{2S}{BC}$ = $\frac{2.10\sqrt{3}}{11,4}$ $\approx$ 3,04.