The give diagram represents a right angled triangle with side AB and BC as follows,
[tex]\begin{gathered} AB=24 \\ BC=7 \end{gathered}[/tex]Apply the Pythagoras Theorem and solve for the hypotenuse,
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2=(24)^2+(7)^2 \\ AC^2=576+49 \\ AC^2=625 \\ AC=\sqrt[]{625} \\ AC=25 \end{gathered}[/tex]Now, apply the cosine ratio for angle A as follows,
[tex]\begin{gathered} \cos A=\frac{AB}{AC} \\ \cos A=\frac{24}{25} \end{gathered}[/tex]Thus, the cosine of angle A is equal to 24/25 .
