Find, correct to the nearest degree, the three angles of the triangle with the given vertices

AB = (5,-3,0) - (1,0,-1) = (4,-3,1)
AC= (1,5,2) - (1,0,-1) = (0,5,3)
|AB| = sqrt (4^2+3^2+1^2) = sqrt(26)
|AC| = sqrt (0 + 5^2+3^2) = sqrt(34)

use:
AB.AC = |AB|*|AC| cos ∠CAB
(4,-3,1).(0,5,3) = sqrt(26)*sqrt(34)* cos ∠CAB
4*0 -3*5 +1*3 = sqrt(26)*sqrt(34)* cos ∠CAB
-12 = sqrt(26)*sqrt(34)* cos ∠CAB
cos ∠CAB = - 0.404
∠CAB = 113.8 degree

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BA = (1,0,-1) - (5,-3,0) = (-4,3,-1)
BC= (1,5,2)-(5,-3,0) = (-4,8,2)
|BA| = sqrt(26)
|BC| = sqrt (4^2 + 8^2 + 2^2) = sqrt(84)

use:
BA.BC = |BA|*|BC|* cos ∠ABC
(-4,3,-1).(-4,8,2) = sqrt(26) * sqrt(84) * cos ∠ABC
16+24-2 = sqrt(26) * sqrt(84) * cos ∠ABC
cos ∠ABC -= 0.813
∠ABC = 35.6 degree

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sum of all angle = 180
∠BCA + 35.6 + 113.8 = 180
∠BCA = 30.6 degree