1. **State the problem:** We need to find the length of side $x$ in a triangle where one side is 6.2 cm, and the angles adjacent to this side are 65° and 51°. 2. **Identify the known elements:** - Side opposite 65° is 6.2 cm. - Angle opposite side $x$ is 51°. - The third angle can be found since the sum of angles in a triangle is 180°. 3. **Calculate the third angle:** $$180^\circ - 65^\circ - 51^\circ = 64^\circ$$ 4. **Use the Law of Sines formula:** $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ Where $a$, $b$, and $c$ are sides opposite angles $A$, $B$, and $C$ respectively. 5. **Assign values:** - Let side $a = x$ opposite angle $A = 51^\circ$. - Side $b = 6.2$ cm opposite angle $B = 65^\circ$. 6. **Apply Law of Sines to find $x$:** $$\frac{x}{\sin 51^\circ} = \frac{6.2}{\sin 65^\circ}$$ 7. **Solve for $x$:** $$x = \frac{6.2 \times \sin 51^\circ}{\sin 65^\circ}$$ 8. **Calculate sine values:** $$\sin 51^\circ \approx 0.7771$$ $$\sin 65^\circ \approx 0.9063$$ 9. **Compute $x$:** $$x = \frac{6.2 \times 0.7771}{0.9063} \approx \frac{4.817}{0.9063} \approx 5.315$$ 10. **Final answer:** The length of side $x$ is approximately **5.32 cm**.