An extra: Finding a side given two sides, but the corresponding angle is NOT an included angle.
In general, when we know two sides and any angle, we can always find the third side with the cosine rule. But when the angle is not sandwiched between the two known sides, but rather the unknown side helps cut it off, I found things get somewhat more bizarre.
(https://i.imgur.com/fbe1Jeo.jpg)
Plugging into the cosine rule gives me
\begin{align*}
2^2 &= 4^2 + x^2 - 2\times 4\times x \times \cos 16^\circ\\
0 &= x^2 - (8\cos 16^\circ)x + 12
\end{align*}
...well then, it's a quadratic! And not a pleasant one.
\begin{align*}
x &= \frac{8\cos 16^\circ \pm \sqrt{64\cos^2 16^\circ - 48}}{2}\\
&\approx 5.51, \, 2.18
\end{align*}
What is going on here? Apparently there's TWO possible values for the length \(x\)?
This illustrates what's commonly known as the ambiguous case for the COsine rule. As this is not in your syllabus, we don't delve into it much here. If you're really interested, check out
this page I found.