Remember:
Some Old Hags, Sin=Opp/Hyp
Can't Always Hide, Cos=Adj/Hyp
Their Old Age. Tan=Opp/Adj
You have adj and hyp so the ratio is Cos.
Now if you want to find an angle you must use inverse trig. That is $$Cos^{-1}$$ but the Web2 site calc does not have that. Arc tan is exactly the same thing! So use acos 
acos(adj/hyp) = acos(13/23)
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{13}}}{{\mathtt{23}}}}\right)} = {\mathtt{55.582\: \!611\: \!289\: \!558^{\circ}}}$$
.