The figure shows a triangle \(ABC\) where \(BC = 23\) cm, \(K\) lies on \(BC\) such that the length of \(BK\) is \(135\%\) of the length of \(KC\) and \(\angle AKC = 90^\circ\). Given that the area of \(\Delta ABK\) is \(68\text{ cm}^2\), find \(\angle BAC\).

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