Answer: The cosine of angle A is [tex]\dfrac{8\sqrt{89}}{89}.[/tex]
Step-by-step explanation: We are given to find the value of cosine for angle A from the figure.
From the figure, we see that
triangle ABC is a right-angled triangle with ∠C = 90° and hypotenuse AB.
Also, AB = 8 ft and BC = 5 ft.
Using Pythagoras theorem in right-angled triangle ABC, we have
[tex]AB^2=AC^2+BC^2\\\\\Rightarrow AB^2=8^2+5^2\\\\\Rightarrow AB=\sqrt{64+25}\\\\\Rightarrow AB=\sqrt{89}.[/tex]
Therefore, we get
[tex]\cos \angle A=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos \angle A=\dfrac{AC}{AB}\\\\\\\Rightarrow \cos\angle A=\dfrac{8}{\sqrt{89}}\\\\\\\Rightarrow \cos\angle A=\dfrac{8\sqrt{89}}{89}.[/tex]
Thus, the cosine of angle A is [tex]\dfrac{8\sqrt{89}}{89}.[/tex]
