1. **State the problem:** We have a right triangle with angles 80° and 70°, and the side opposite the 70° angle is 8.8 cm. We need to find the length $x$ of the side opposite the 80° angle. 2. **Recall the triangle angle sum rule:** The sum of angles in a triangle is 180°. Here, the right angle is 30° (since 80° + 70° = 150°, the right angle must be 30° to make 180°). But this contradicts the right triangle definition. Actually, the problem states a right triangle with angles 80° and 70°, which is impossible because 80° + 70° = 150°, leaving 30° for the right angle, which is not 90°. So the triangle is not right-angled. Let's assume the triangle is not right-angled but has angles 80° and 70° and the side opposite 70° is 8.8 cm. 3. **Use the Law of Sines:** The Law of Sines states: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, $c$ are sides opposite angles $A$, $B$, $C$ respectively. 4. **Assign sides and angles:** Let $x$ be the side opposite the 80° angle, and 8.8 cm opposite the 70° angle. 5. **Apply Law of Sines:** $$\frac{x}{\sin 80^\circ} = \frac{8.8}{\sin 70^\circ}$$ 6. **Solve for $x$:** $$x = \frac{8.8 \times \sin 80^\circ}{\sin 70^\circ}$$ 7. **Calculate values:** $$\sin 80^\circ \approx 0.9848, \quad \sin 70^\circ \approx 0.9397$$ 8. **Substitute and compute:** $$x = \frac{8.8 \times 0.9848}{0.9397} \approx \frac{8.666}{0.9397} \approx 9.22$$ **Final answer:** $$x \approx 9.22 \text{ cm}$$