Representing the information in a diagram, we have:
The given sides are hypotenuse=6 and opposite=4.
The trigonometry ratio Cos is given as:
[tex]\text{Cos A=}\frac{Adjacent}{\text{Hypotenuse}}[/tex]
We will use the pythagoras theorem to obtain the adjacent side.
Thus, we have:
[tex]\begin{gathered} H^2=A^2+O^2 \\ 6^2=A^2+4^2 \\ 36=A^2+16 \\ 36-16=A^2 \\ 20=A^2 \\ A=\sqrt[]{20} \\ A=4.472 \end{gathered}[/tex]
The Cos A is :
[tex]\begin{gathered} \text{Cos A=}\frac{Adjacent}{\text{Hypotenuse}} \\ \text{Cos }A=\frac{4.472}{6} \\ \text{Cos A=0.745} \end{gathered}[/tex]
Hence, Cos A is 0.745
