Notam latura cubului=a
DC=a
B'C=a√2
[tex]CO=\frac{a\sqrt{2} }{2}[/tex]
In ΔDOC dr in C, aplicam Pitagora
DO²=DC²+CO²
[tex]DO^2=a^2+\frac{2a^2}{4} =\frac{6a^2}{4} \\\\DO=\frac{a\sqrt{6} }{2}[/tex]
DO=BO'
O'=A'D∩AD'
AB║CD
AO'║BO⇒ DO║BO'
∡(DO,A'B)=∡(BO',A'B)=∡A'BO'
A'B=a√2
[tex]BO'=\frac{a\sqrt{6} }{2}[/tex]
[tex]A'O'=\frac{a\sqrt{2} }{2}[/tex]
[tex]2a^2=\frac{6a^2}{4} +\frac{2a^2}{4} \\\\2a^2=2a^2[/tex]⇒R.Pitagora
ΔA'BO' dr in O'
[tex]cosA'BO'=\frac{BO'}{A'B} =\frac{\frac{a\sqrt{6} }{2} }{a\sqrt{2} }=\frac{\sqrt{3} }{2}[/tex]