find the angles of the triangle with vertices A:(0,0,0), B:(4,2,1), C:(1,2,4)

Question

i need the answer of this quistion

Answer 1

The length of AB is sqrt(16+4+1)=sqrt(21)=AC (Pythagoras' theorem). This is an isosceles triangle. BC=sqrt((4-1)^2+0+(4-1)^2)=sqrt(18)=3sqrt(2). Angles B and C are equal, and cosB=(1/2)3sqrt(2)/sqrt(21)=0.46291, B=C=62.425 degrees. So angle A=55.15 degrees. (Figures approximate.)