ANSWER
cos A = √20/6 ≈ 0.75
EXPLANATION
Triangle ABC is:
Since this is a right triangle we can use the trigonometric ratios to find cosA:
[tex]\cos A=\frac{\text{adjacent side}}{hypotenuse}[/tex]
the hypotenuse of this triangle is side c, and the adjacent side is side b. We don't have side b, but we have two sides and again, as this is a right triangle, we can use the Pythagorean theorem to find the missing side:
[tex]\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{6^2-4^2} \\ b=\sqrt[]{36-16} \\ b=\sqrt[]{20} \end{gathered}[/tex]
The cosine of A is then:
[tex]\cos A=\frac{b}{c}=\frac{\sqrt[]{20}}{6}[/tex]
Rounded to the nearest hundredth:
[tex]\cos A\approx0.75[/tex]
