1. **Stating the problem:** We have a triangle with one angle of 30° at the bottom-left corner, and two sides adjacent to this angle measuring 10 and 6 units respectively. We want to find the length of the base (the side opposite the 30° angle). 2. **Formula used:** To find the length of the side opposite a known angle when two sides and the included angle are known, we use the Law of Cosines: $$c^2 = a^2 + b^2 - 2ab \cos(C)$$ where $c$ is the side opposite angle $C$, and $a$, $b$ are the other two sides. 3. **Applying the formula:** Here, $a=10$, $b=6$, and $C=30^\circ$. $$c^2 = 10^2 + 6^2 - 2 \times 10 \times 6 \times \cos(30^\circ)$$ 4. **Calculate each term:** $$10^2 = 100$$ $$6^2 = 36$$ $$2 \times 10 \times 6 = 120$$ $$\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$$ 5. **Substitute values:** $$c^2 = 100 + 36 - 120 \times 0.866$$ $$c^2 = 136 - 103.92 = 32.08$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{32.08} \approx 5.66$$ **Final answer:** The length of the base opposite the 30° angle is approximately **5.66** units.