Đáp án:
\[\cos A = \dfrac{{ - 7}}{{\sqrt {85} }}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A\left( {1;2} \right);\,\,\,B\left( { - 1;1} \right);\,\,\,\,C\left( {5;1} \right)\\
\Rightarrow \left\{ \begin{array}{l}
\overrightarrow {AB} = \left( { - 2;\,\, - 1} \right)\\
\overrightarrow {BC} = \left( {6;0} \right)\\
\overrightarrow {CA} = \left( { - 4;\,\,1} \right)
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
AB = \sqrt {{{\left( { - 2} \right)}^2} + {{\left( { - 1} \right)}^2}} = \sqrt 5 \\
BC = \sqrt {{6^2} + {0^2}} = 6\\
CA = \sqrt {{{\left( { - 4} \right)}^2} + {1^2}} = \sqrt {17}
\end{array} \right.\\
\cos A = \dfrac{{A{B^2} + A{C^2} - B{C^2}}}{{2.AB.AC}} = \dfrac{{{{\left( {\sqrt 5 } \right)}^2} + {{\left( {\sqrt {17} } \right)}^2} - {6^2}}}{{2.\sqrt 5 .\sqrt {17} }} = \dfrac{{ - 7}}{{\sqrt {85} }}
\end{array}\)
