The cosine of an angle theta in a right triangle is given by its adjacent side divided by the hypotenuse:
[tex]\cos \theta=\frac{x}{r}[/tex]
We don't know the value of r but with x, y and the Pythagorean Theorem we can find it:
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2}=\sqrt[]{3^2+6^2}=\sqrt[]{9+36}=\sqrt[]{45} \\ r=6.71 \end{gathered}[/tex]
Then the cosine we are looking for is:
[tex]\cos \theta=\frac{x}{r}=\frac{3}{6.71}=0.45[/tex]
Then the correct option is the second one since:
[tex]\frac{\sqrt[]{5}}{5}=0.45[/tex]
