1. **State the problem:** We have triangle $\triangle HIJ$ with side $h = 97$ cm opposite angle $H$, angle $H = 144^\circ$, and angle $I = 24^\circ$. We need to find the length of side $i$ opposite angle $I$. 2. **Find the missing angle:** The sum of angles in a triangle is $180^\circ$. $$J = 180^\circ - H - I = 180^\circ - 144^\circ - 24^\circ = 12^\circ$$ 3. **Use the Law of Sines:** The Law of Sines states: $$\frac{h}{\sin H} = \frac{i}{\sin I} = \frac{j}{\sin J}$$ We want to find $i$, so: $$i = h \times \frac{\sin I}{\sin H}$$ 4. **Calculate the sines:** $$\sin 144^\circ = \sin(180^\circ - 36^\circ) = \sin 36^\circ \approx 0.5878$$ $$\sin 24^\circ \approx 0.4067$$ 5. **Substitute values and calculate $i$:** $$i = 97 \times \frac{0.4067}{0.5878}$$ Show intermediate cancellation: $$i = 97 \times \cancel{\frac{0.4067}{0.5878}}$$ Calculate the fraction: $$\frac{0.4067}{0.5878} \approx 0.6921$$ So: $$i \approx 97 \times 0.6921 = 67.13$$ 6. **Round to the nearest tenth:** $$i \approx 67.1 \text{ cm}$$ **Final answer:** The length of side $i$ is approximately $67.1$ cm.