Triangle

Geometry Level 4

See the picture above. It is known AB=3 cm\overrightarrow{AB}=3\text{ cm}, AC=303 cm\overrightarrow{AC}=\dfrac{\sqrt{30}}{3}\text{ cm}, AD=4 cm\overrightarrow{AD}=4\text{ cm}, and BC=2 cm\overrightarrow{BC}=2\text{ cm}. If BAD=α\angle BAD=\alpha, then sinα=pq. \sin\alpha=\frac{\sqrt{p}}{q}. Calculate pq\,p-q.

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