Gọi \(O\) là trọng tâm tam giác \(ABC\).
\(\begin{array}{l} \Rightarrow SO \bot \left( {ABC} \right)\\ \Rightarrow \left( {SA,\left( {ABC} \right)} \right) = \left( {SA,OA} \right) = \widehat {SAO},\\\left( {SB,\left( {ABC} \right)} \right) = \left( {SB,OB} \right) = \widehat {SBO},\\\left( {SC,\left( {ABC} \right)} \right) = \left( {SC,OC} \right) = \widehat {SCO}\end{array}\)
Tam giác \(ABC\) đều \( \Rightarrow OA = OB = OC\).
\(\begin{array}{l}SA = SB = SC \Rightarrow \frac{{OA}}{{SA}} = \frac{{OB}}{{SB}} = \frac{{OC}}{{SC}} \Rightarrow \cos \widehat {SAO} = \cos \widehat {SBO} = {\mathop{\rm co}\nolimits} \widehat {sSCO}\\ \Rightarrow \left( {SA,\left( {ABC} \right)} \right) = \left( {SB,\left( {ABC} \right)} \right) = \left( {SC,\left( {ABC} \right)} \right)\end{array}\)
