Найдем длины сторон.
|AB|^2 = (-2-8)^2 + (-1+1)^2 + (4+1)^2 = (-10)^2 + 0^2 + 5^2 = 100 + 0 + 25 = 125
|AB| = sqrt(125) = 5*sqrt(5)
|AC|^2 = (1-8)^2 + (-1+1)^2 + (0+1)^2 = (-7)^2 + 0^2 + 1^2 = 49 + 0 + 1 = 50
|AC| = sqrt(50) = 5*sqrt(2)
|BC|^2 = (1+2)^2 + (-1+1)^2+ (0-4)^2 = 3^2 + 0^2 + 4^2 = 9 + 16 = 25
|BC| = sqrt(25) = 5
По теореме косинусов:
|AB|^2 = |AC|^2 + |BC|^2 - 2*|AC|*|BC|*cos C
125 = 50 + 25 - 2*5*sqrt(2)*5*cos C
125 - 50 - 25 = -2*5*5*sqrt(2)*cos C
50 = -50*sqrt(2)*cos C
cos C = -1/sqrt(2)
С = 3π/4 = 135°