a/ \(SO\perp\left(ABCD\right)\Rightarrow\widehat{SAO}\) là góc giữa SA và (ABCD)
\(AC=\sqrt{AB^2+BC^2}=a\sqrt{5}\Rightarrow AO=\frac{a\sqrt{5}}{2}\)
\(cos\widehat{SAO}=\frac{AO}{SA}=\frac{\sqrt{5}}{6}\Rightarrow\widehat{SAO}\approx68^07'\)
b/ \(SO\perp\left(ABCD\right)\Rightarrow\widehat{SKO}\) là góc giữa SK và (ABCD)
\(OK=\frac{1}{2}BC=a\) ; \(SO=\sqrt{SA^2-OA^2}=\frac{a\sqrt{31}}{2}\)
\(\Rightarrow tan\widehat{SKO}=\frac{SO}{OK}=\frac{\sqrt{31}}{2}\Rightarrow\widehat{SKO}\approx70^014'\)
c/ \(OK\perp CD;MN//CD\Rightarrow OK\perp MN\)
\(SO\perp\left(ABCD\right)\Rightarrow SO\perp OK\Rightarrow OK\perp\left(SMN\right)\)
\(\Rightarrow\widehat{KSO}\) là góc giữa SK và (SMN)
\(tan\widehat{KSO}=\frac{OK}{SO}=\frac{2}{\sqrt{31}}\Rightarrow\widehat{KSO}\approx19^045'\)
