YX=(2,-2,7)+(0,3,4)=(2,1,11) and YZ=(0,3,4)+(2/5,-2/5,7/5)=(2/5,13/5,27/5).
XZ=(2,-2,7)+(2/5,13/5,27/5)=(6/5)(2,-2,7). XYZ form a triangle XYZ.
YX^2=4+1+121=126; YZ^2=(4+169+729)/25=902/25; XZ^2=36(4+4+49)/25=2052/25.
XZ^2=YX^2+YZ^2-2YX.YZcosY (cosine rule).
D=Dot product=YX.YZcosY=(YX^2+YZ^2-XZ^2)/2=(126+902/25-2052/25)/2=80/2=40.
YX.YZ=(2,1,11).(2/5,13/5,27/5)=(4+13+297)/5=314/5, so cosY=5D/314=100/157=0.6369 approx, Y=50.44° approx.