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?

Emilio Novati · Accepted Answer · 2016-11-06T14:16:33.057

0

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.

edited Nov 06 '16 at 14:16

answered Nov 06 '16 at 13:37

Emilio Novati

62,675

Emilio, is $\triangle{ACD}$ right triangle that you can use $\sin{\angle ACD}$? :D I have linkpicture[/link] of a rhombus and I don't see $\triangle ACD$ is right triangle? – andrej benedičič Nov 06 '16 at 13:55
No, $ACD$ is not a right triangle. But, if $AH=h$ is the height of the rhombus from $A$ to the side $CD$, than $ACH$ is a right triangle and $\angle ACH=\angle ACD$. – Emilio Novati Nov 06 '16 at 13:59
linkpicture of my rhombus[/link] ... Can you upload your image? :D – andrej benedičič Nov 06 '16 at 14:05
I have added a figure. It's essentially the same as your. – Emilio Novati Nov 06 '16 at 14:13
Cool, cool. ;) Thanks. I figure it out. ;) – andrej benedičič Nov 06 '16 at 14:45

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

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