Convert a 3D vector into a vertical angle

If we take just the horizontal component x and z, the magnitude of that is:

m=Sqr(x*x+z*z)
m=Sqr(0.577350259^2.0+0.577350259^2.0)
m=Sqr(0.333333333+0.333333333)
m=Sqr(0.66666666)
m=0.8165

Now normalize just the horizontal vector:
x=0.5774/0.8165
x=0.7072
z=0.5774/0.8165
z=0.7072

So now we have a triangle with 0.8165 as the base, the hypotonuse is 1, and the height is 0.5774? Why does this seem so hard?