1. The problem asks for the expression for the length \(AC\) in triangle \(ABC\).\n\n2. Given: \(\triangle ABC\) is a right triangle with right angle at \(B\), \(\angle BAC = 50^\circ\), \(CB = 40\) cm, and \(AC\) as the hypotenuse opposite the \(50^\circ\) angle.\n\n3. Since \(AC\) is the hypotenuse, and \(CB\) is adjacent to \(50^\circ\), we use the cosine function: \n\n$$\cos 50^\circ = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{CB}{AC} = \frac{40}{AC}$$\n\n4. Rearranging for \(AC\):\n\n$$AC = \frac{40}{\cos 50^\circ}$$\n\n5. Therefore, the length \(AC\) is expressed as \(\displaystyle 40 \div \cos 50^\circ\), which corresponds to option B.