1. **State the problem:** We have two similar right triangles \(\triangle ABC \sim \triangle YXZ\) with a right angle at \(C\) in \(\triangle ABC\) and at \(Z\) in \(\triangle YXZ\). We need to find \(\cos X\), \(\sin X\), and \(\tan X\) in \(\triangle YXZ\).\n\n2. **Recall similarity and trigonometric definitions:** Since the triangles are similar, corresponding angles are equal, so angle \(X\) in \(\triangle YXZ\) corresponds to angle \(A\) in \(\triangle ABC\).\n\n3. **Identify sides in \(\triangle ABC\):** Given \(BC=13.6\), \(AC=25.5\), and \(AB=28.9\) with right angle at \(C\). Hypotenuse is \(AB=28.9\).\n\n4. **Calculate \(\cos A\), \(\sin A\), and \(\tan A\) in \(\triangle ABC\):**\n- \(\cos A = \frac{\text{adjacent side to } A}{\text{hypotenuse}} = \frac{AC}{AB} = \frac{25.5}{28.9}\)\n- \(\sin A = \frac{\text{opposite side to } A}{\text{hypotenuse}} = \frac{BC}{AB} = \frac{13.6}{28.9}\)\n- \(\tan A = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{BC}{AC} = \frac{13.6}{25.5}\)\n\n5. **Simplify fractions and calculate values:**\n\[\cos A = \frac{25.5}{28.9} \approx 0.8824 \to 0.88\]\n\[\sin A = \frac{13.6}{28.9} \approx 0.4702 \to 0.47\]\n\[\tan A = \frac{13.6}{25.5} \approx 0.5333 \to 0.53\]\n\n6. **Since \(X\) corresponds to \(A\), the trigonometric ratios are:**\n\[\cos X = 0.88, \quad \sin X = 0.47, \quad \tan X = 0.53\]