1. **Problem statement:** We have a triangle with sides 22 cm and 14 cm, and an angle of 35° opposite the 22 cm side. We need to find the angle $x$ at the bottom left corner. 2. **Formula used:** We use the Law of Sines, which 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. 3. **Assign known values:** - Side $a = 22$ cm opposite angle $A = 35^\circ$ - Side $b = 14$ cm opposite angle $B = x$ 4. **Apply Law of Sines:** $$\frac{22}{\sin 35^\circ} = \frac{14}{\sin x}$$ 5. **Solve for $\sin x$:** $$\sin x = \frac{14 \times \sin 35^\circ}{22}$$ 6. **Calculate $\sin 35^\circ$:** $$\sin 35^\circ \approx 0.574$$ 7. **Substitute and simplify:** $$\sin x = \frac{14 \times 0.574}{22} = \frac{8.036}{22}$$ 8. **Simplify fraction:** $$\sin x = \frac{\cancel{8.036}}{\cancel{22}} \approx 0.365$$ 9. **Find angle $x$:** $$x = \sin^{-1}(0.365) \approx 21.4^\circ$$ 10. **Round to nearest whole number:** $$x \approx 21^\circ$$ **Final answer:** The value of angle $x$ is approximately $21^\circ$.