Hello, ZettaDigit!

The problem is the dreaded "ambiguous case".

There are *two* solutions.

Find angle $\displaystyle x.$ Code:

C o - - - - - - - - - - - o D
\ * \
\ x * \
\ * \
\ 5 * \
\ * \
\ * \
\ 29° * \
A o - - - - - - - - - - - o B
8

Law of Sines: .$\displaystyle \frac{\sin x}{8} \:=\:\frac{\sin29^o}{5} \quad\Rightarrow\quad \sin x \:=\:\frac{8\sin29^o}{5} \:=\: 0.775695392$

Therefore: .$\displaystyle x \:\approx\:\boxed{50.9^o}$

But inverse sine can have more than one value.

Hence: .$\displaystyle x \:=\:180^o - 50.9^o \;=\;\boxed{129.1^o}$

And the parallelogram looks like this:

Code:

C * - - - - - - - - - - - - - - - - - - - * D
/ * /
/ 129.1° * /
/ * /
5 / * /
/ * /
/ * /
/ 29° * /
A * - - - - - - - - - - - - - - - - - - - * B
8