Угол С = 180 - 30 - 45 = 105 градусов. По теореме синусов. 1. AB / sin (C) = AC / sin(B) AC = AB * sin (B) / sin (C) = 8 * (√2/2) / ((1 + √3) / 2√2) = 16 / (1 + √3) 2. AB / sin (C) = BC / sin (A) BC = AB * sin (A) / sin (C) = 8 * (1/2) / ((1 + √3) / 2√2) = 8 * √2 / (1 + √3)
По теореме синусов.
1. AB / sin (C) = AC / sin(B)
AC = AB * sin (B) / sin (C) = 8 * (√2/2) / ((1 + √3) / 2√2) = 16 / (1 + √3)
2. AB / sin (C) = BC / sin (A)
BC = AB * sin (A) / sin (C) = 8 * (1/2) / ((1 + √3) / 2√2) = 8 * √2 / (1 + √3)
АВ/sin105°=BC/sin30°,
8/0.97=BC/0,5.
BC=8·0,5/0,97=4/0,98=4,1 л. ед.
ВС/sin30°=AC/sin45°,
4,1/0,5=AC/√2/2,
AC=4,1·0,71/0,5=5.8 л. ед.