How to find inner angles and side of the rhombus given height and diagonal AC

Question

I have to find inner angles $\alpha$, $\beta$, $\delta$ and $\gamma$, other diagonal $\left|BD\right|$ and length of a side $a$ into a rhombus where is given the height $h = 2\sqrt{3} cm$ and the diagonal $\left|AC\right| = 4\sqrt{3} cm$.

How would I find this? :D Can you help me somebody? :)

I tried with $\sin{\alpha} = \frac{h}{a}$, but I still haven't found the solution. Somebody?

Answer 1

Hint:

note that

$$ \sin (\angle ACD)=\frac{h}{\overline{AC}}=\frac{1}{2} $$

From this you can find the side an the other diagonal of the rhombus.