1. **Problem statement:** Calculate the length $x$ in the given triangle with angles 70°, 20°, and side lengths 7 and 4. 2. **Formula used:** Use the Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a,b,c$ are sides opposite angles $A,B,C$ respectively. 3. **Identify known values:** Given angles 70° and 20°, the third angle is $$180^\circ - 70^\circ - 20^\circ = 90^\circ$$. 4. **Assign sides:** Let side opposite 70° be 7, side opposite 20° be 4, and side opposite 90° be $x$. 5. **Apply Law of Sines:** $$\frac{7}{\sin 70^\circ} = \frac{4}{\sin 20^\circ} = \frac{x}{\sin 90^\circ}$$ 6. **Calculate $x$:** $$x = \frac{7}{\sin 70^\circ} \times \sin 90^\circ$$ 7. **Evaluate sines:** $$\sin 70^\circ \approx 0.9397, \quad \sin 90^\circ = 1$$ 8. **Calculate $x$ value:** $$x = \frac{7}{0.9397} \times 1 \approx 7.45$$ 9. **Final answer:** $$\boxed{x \approx 7.45}$$