\(SA\perp\left(ABCD\right)\Rightarrow\widehat{SCA}\) là góc giữa SC và (ABCD)
\(AC=AB\sqrt{2}=a\sqrt{2}\Rightarrow tan\widehat{SCA}=\frac{SA}{AC}=\frac{1}{\sqrt{3}}\)
\(\Rightarrow\widehat{SCA}=30^0\)
b/ \(SA\perp\left(ABCD\right)\Rightarrow SA\perp BC\)
Mà \(BC\perp AB\Rightarrow BC\perp\left(SAB\right)\)
\(\Rightarrow\widehat{CSB}\) là góc giữa SC và (SAB)
\(SB=\sqrt{SA^2+AB^2}=a\sqrt{7}\)
\(\Rightarrow tan\widehat{CSB}=\frac{SB}{BC}=\sqrt{7}\Rightarrow\widehat{CSB}\approx69^017'\)
c/ Kẻ \(AH\perp SB\Rightarrow AH\perp\left(SBC\right)\)
\(\Rightarrow\widehat{ACH}\) là góc giữa AC và (SBC)
\(\frac{1}{AH^2}=\frac{1}{SA^2}+\frac{1}{AB^2}\Rightarrow AH=\frac{SA.AB}{\sqrt{SA^2+AB^2}}=\frac{a\sqrt{14}}{4}\)
\(\Rightarrow sin\widehat{ACH}=\frac{AH}{AC}=\frac{\sqrt{7}}{4}\Rightarrow\widehat{ACH}\approx41^024'\)
