\(\cos \theta = \frac{5}{13}\)

\(\implies\) In the right- angled triangle, with an angle \(\theta\), the adjacent side to \(\theta\) = 5 and the hypotenuse = 13.

\(\therefore 13^2 = opp^2 + 5^2\)

\(opp^2 = 169 - 25 = 144 \implies opp = \sqrt{144}\)

= 12.

\(\tan \theta = \frac{opp}{adj} = \frac{12}{5}\)