1. **Problem statement:** We have a triangle with one angle measuring 116° and two sides adjacent to this angle measuring 2.7 cm and 4.9 cm. We need to find the unknown angle $x$ opposite the side labeled $x$. 2. **Formula used:** We will use the Law of Cosines to find the length of side $x$ first: $$x^2 = a^2 + b^2 - 2ab \cos(C)$$ where $a=2.7$, $b=4.9$, and $C=116^\circ$. 3. **Calculate $x^2$:** $$x^2 = 2.7^2 + 4.9^2 - 2 \times 2.7 \times 4.9 \times \cos(116^\circ)$$ Calculate each term: $$2.7^2 = 7.29$$ $$4.9^2 = 24.01$$ $$\cos(116^\circ) \approx -0.4384$$ So, $$x^2 = 7.29 + 24.01 - 2 \times 2.7 \times 4.9 \times (-0.4384)$$ Calculate the product: $$2 \times 2.7 \times 4.9 = 26.46$$ Then, $$x^2 = 7.29 + 24.01 + 26.46 \times 0.4384$$ $$x^2 = 31.3 + 11.6 = 42.9$$ 4. **Find $x$:** $$x = \sqrt{42.9} \approx 6.55$$ 5. **Find the unknown angle $x$ using Law of Sines:** $$\frac{\sin(x)}{a} = \frac{\sin(C)}{x}$$ Rearranged: $$\sin(x) = \frac{a \sin(C)}{x} = \frac{2.7 \times \sin(116^\circ)}{6.55}$$ Calculate $\sin(116^\circ) \approx 0.8829$: $$\sin(x) = \frac{2.7 \times 0.8829}{6.55} = \frac{2.384}{6.55} \approx 0.364$$ 6. **Calculate angle $x$:** $$x = \sin^{-1}(0.364) \approx 21.3^\circ$$ 7. **Round to nearest degree:** $$x \approx 21^\circ$$ **Answer:** The unknown angle is approximately 21°, which is closest to option a. 22°.