\(SA\perp\left(ABCD\right)\Rightarrow\left\{{}\begin{matrix}SA\perp AB\\SA\perp AD\end{matrix}\right.\) \(\Rightarrow\) các tam giác SAB và SAD vuông tại A
\(\left\{{}\begin{matrix}SA\perp\left(ABCD\right)\Rightarrow SA\perp BC\\BC\perp AB\end{matrix}\right.\) \(\Rightarrow BC\perp\left(SAB\right)\Rightarrow BC\perp SB\)
\(\Rightarrow\Delta SBC\) vuông tại B
\(\left\{{}\begin{matrix}SA\perp\left(ABCD\right)\Rightarrow SA\perp CD\\CD\perp AD\end{matrix}\right.\) \(\Rightarrow CD\perp\left(SAD\right)\) \(\Rightarrow CD\perp SD\)
\(\Rightarrow\Delta SCD\) vuông tại D
b/ \(\left\{{}\begin{matrix}SA\perp\left(ABCD\right)\Rightarrow SA\perp BD\\BD\perp AC\end{matrix}\right.\) \(\Rightarrow BD\perp\left(SAC\right)\)
\(SO\in\left(SAC\right)\Rightarrow BD\perp SO\)
c/ \(SA\perp\left(ABCD\right)\Rightarrow\widehat{SCA}\) là góc giữa SC và (ABCD)
\(AC=a\sqrt{2}\Rightarrow tan\widehat{SCA}=\frac{SA}{AC}=\sqrt{3}\Rightarrow\widehat{SCA}=60^0\)
\(SA\perp\left(ABCD\right)\Rightarrow\widehat{SOA}\) là góc giữa SO và (ABCD)
\(AO=\frac{1}{2}AC=\frac{a\sqrt{2}}{2}\) \(\Rightarrow tan\widehat{SOA}=\frac{SA}{AO}=2\sqrt{3}\Rightarrow\widehat{SOA}\approx74^0\)
