1. **State the problem:** We need to solve for $x$, the length of side CE in right triangle CDE, where angle $C = 17^\circ$, angle $D = 90^\circ$, and side DE (opposite angle $C$) is 1.7 units. 2. **Identify the sides relative to angle $C$:** - Side DE is opposite angle $C$. - Side CE is adjacent to angle $C$. - Side CD is the hypotenuse. 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Apply the formula:** $$\tan(17^\circ) = \frac{DE}{CE} = \frac{1.7}{x}$$ 5. **Solve for $x$:** $$x = \frac{1.7}{\tan(17^\circ)}$$ 6. **Calculate $\tan(17^\circ)$:** $$\tan(17^\circ) \approx 0.3057$$ 7. **Compute $x$:** $$x = \frac{1.7}{0.3057} \approx 5.56$$ 8. **Round to the nearest tenth:** $$x \approx 5.6$$ **Final answer:** $x = 5.6$ units.