In order to find the cosine of theta, first let's find the length of the third side of the triangle, using Pythagorean theorem:
[tex]\begin{gathered} 13^2=12^2+x^2 \\ 169=144+x^2 \\ x^2=169-144 \\ x^2=25 \\ x=5 \end{gathered}[/tex]
The cosine relation is given by the length of the adjacent side to the angle over the length of the hypotenuse.
So we have:
[tex]\cos (\theta)=\frac{5}{13}[/tex]
