1. The problem states that in a geometric figure with points C, D, A, B, and E, we know the lengths $DA = 13.7$, $EB = 17.1$, and $CD = 18.3$. We are asked to find the length $CE$. 2. Notice that triangle $CDA$ contains a smaller triangle $CEB$ inside it. These two triangles share angle relationships and are similar by the AA similarity criterion because $\angle CDA = \angle CEB$ and $\angle DAC = \angle EBC$ (corresponding angles in the figure). 3. Since the triangles $CDA$ and $CEB$ are similar, the sides are proportional. So the ratios between corresponding sides are equal: $$\frac{CD}{CE} = \frac{DA}{EB}$$ 4. Substitute the known lengths: $$\frac{18.3}{CE} = \frac{13.7}{17.1}$$ 5. Solve for $CE$ by cross multiplying: $$18.3 \times 17.1 = 13.7 \times CE$$ $$CE = \frac{18.3 \times 17.1}{13.7}$$ 6. Calculate the numerator: $$18.3 \times 17.1 = 313.0$$ 7. Divide by 13.7 to find $CE$: $$CE = \frac{313.0}{13.7} \approx 22.9$$ 8. The length $CE$ rounded to the nearest tenth is $22.9$. **Final answer:** $$CE = 22.9$$