A trigonometry based triangle problem

Question

In the triangle ABC below, side a is 10 units, and side b is 12 units. cos(angleACB) = 1/5. Find the value of cos(angleCBA). I'm pretty sure that I should use the law of sines, or the law of cosines, but I need help as to which and how they can directly apply to the problem.

Answer 1

Hint:
(i) Use cosine rule to find side $c$ [using $a,b,\angle C$]
(ii) Use cosine rule again to find $\cos(\angle CBA)$ [using $a,c,b]$

The cosine rule is given by $$z^2=x^2+y^2-2xy(\cos\angle Z)$$ where the vertex $Z$ lies between side $x$ and $y$