Soit \( ABCD \) le tétraèdre suivant où \( AB \) vaut \( 9 \), \( AC \) vaut \( 8 \) et
\( \widehat{CAD} = \dfrac{\pi }{3} \).
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Donner la mesure en radian de l'angle \( \widehat{BAC} \) sachant que \( \overrightarrow{AB} \cdot
\overrightarrow{AC} = 54 \).
On donnera uniquement la valeur arrondie au centième, sans unité.