z twierdzenia sinusów:
|AB|/sin120 = 2R
|AB| = 2R sin120 = 2R cos30
|AB| = 4√21/3 * √3/2 = 2√7
z twierdzenia cosinusów:
|AB|² = |AC|² + |BC|² - 2|AC||BC|cos120
28 = |AC|² + 16 + 2|AC|4 sin30
28 = |AC|² + 16 + 2|AC|4 1/2
0 = |AC|² + 4|AC| - 12
Δ = 16 + 48 = 64
√Δ = 8
|AC|₁ = (-4 + 8)/2 = 2
|AC|₂ = (-4 - 8)/2 = -6
|AC| > 0 (bo to długość odcinka)
|AC| = 2
|BC| = 2√7
