# Triangle

Geometry Level 4

See the picture above. It is known $\overrightarrow{AB}=3\text{ cm}$, $\overrightarrow{AC}=\dfrac{\sqrt{30}}{3}\text{ cm}$, $\overrightarrow{AD}=4\text{ cm}$, and $\overrightarrow{BC}=2\text{ cm}$. If $\angle BAD=\alpha$, then $\sin\alpha=\frac{\sqrt{p}}{q}.$ Calculate $\,p-q$.

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