AC^2=AB^2+BC^2
[b]10^2=x^2+y^2[/b]
[b]SB^2[/b]=SA^2-AB^2=10^2-x^2
[b]SB^2[/b]=SC^2-BC^2=(8sqrt(2))^2-y^2
⇒[b] 10^2-x^2=(8sqrt(2))^2-y^2[/b]
Получаем систему уравнений:
{[b]10^2=x^2+y^2[/b]
{[b] 10^2-x^2=(8sqrt(2))^2-y^2[/b]
y=8
x=6
AB=6
BC=8
SD^2=SB^2+BD^2
SB^2=SA^2-AB^2=10^2-x^2=10^2-6^2=64
SD^2=SB^2+BD^2=64+10^2=164
SD=sqrt(164)