1. **State the problem:** We have a triangle with sides 7.1 cm and 8.5 cm, and an angle of 74° between them. We need to find the length of side $b$ opposite the 74° angle. 2. **Formula used:** Use the Law of Cosines, which states: $$b^2 = a^2 + c^2 - 2ac \cos(\theta)$$ where $a=7.1$, $c=8.5$, and $\theta=74^\circ$. 3. **Calculate:** $$b^2 = 7.1^2 + 8.5^2 - 2 \times 7.1 \times 8.5 \times \cos(74^\circ)$$ Calculate each term: $$7.1^2 = 50.41$$ $$8.5^2 = 72.25$$ $$2 \times 7.1 \times 8.5 = 120.7$$ $$\cos(74^\circ) \approx 0.2756$$ 4. **Substitute values:** $$b^2 = 50.41 + 72.25 - 120.7 \times 0.2756 = 122.66 - 33.26 = 89.4$$ 5. **Find $b$:** $$b = \sqrt{89.4} \approx 9.5$$ 6. **Answer:** The length of side $b$ is approximately 9.5 cm to 1 decimal place.