사인·코사인법칙

$\displaystyle {\mathrm{\overline{AB}}} = 3 a$, $\displaystyle {\mathrm{\overline{AC}}} = a$라 하면 $\displaystyle {\mathrm{\overline{BC}}} ^{2} = 9 a ^{2} + a ^{2} - 2 \cdot 3 a \cdot a \cos \frac{\pi}{3}$$= 7 a ^{2}$ $\displaystyle \therefore {\mathrm{\overline{BC}}} = \sqrt{7} a$ $\displaystyle \frac{\mathrm{\overline{BC}}}{\sin \frac{\pi}{3}} = \frac{\sqrt{7} a}{\frac{\sqrt{3}}{2}} = \frac{2 \sqrt{7} a}{\sqrt{3}} = 2 \times 7$ $\displaystyle a = \sqrt{21} = {\mathrm{\overline{AC}}}$