Question 1172059
<br>
You can sanity check your answer by remembering  {{{ -1 <= cos(x) <= 1 }}}, so clearly neither 12 nor 12/5 can be correct.   This is true for sin(x) as well, but not true for tan(x).
<br>

It is often best to draw a triangle for these types of problems.


{{{ drawing(400,200,-1,15,-1,8, grid(0),
            line(0,0,12,0),
            line(12,0,12,5),
            line(0,0,12,5),
           locate(12.2,2.5,"5"),
           locate(6.5,3.5,blue("13")),
           locate(6.2,0.8,"12"),
           locate(1.9,0.8, theta)

) }}}


{{{ tan(theta) = 5/12 }}}  ..... opp/adj
{{{ hypotenuse = sqrt(12^2 + 5^2) = 13 }}}
{{{ cos(theta) = 12/13 }}} ..... adj/hyp

-------------

Just thought to add this, as you might find it helpful.
{{{ tan(theta) = sin(theta)/cos(theta) }}} 

 {{{ sin(theta) = 5/13 }}}  ..... opp/hyp

So, for this problem,  {{{ sin(theta)/cos(theta) }}} = {{{ ((5/13))/((12/13)) }}} = {{{ 5/12 }}}  = {{{ tan(theta) }}}