1. **Problem statement:** We have a right triangle with a 60° angle. The side opposite the 60° angle is $10\sqrt{3}$, the hypotenuse is 20, and the side adjacent to the 60° angle is $x$. We need to find $x$. 2. **Relevant formula:** In a right triangle, the side lengths relate to the angles via trigonometric ratios. For angle $\theta=60^\circ$: - Opposite side = hypotenuse $\times \sin(\theta)$ - Adjacent side = hypotenuse $\times \cos(\theta)$ 3. **Given:** Opposite side = $10\sqrt{3}$, hypotenuse = 20. 4. **Check opposite side with sine:** $$\sin(60^\circ) = \frac{\sqrt{3}}{2}$$ Calculate expected opposite side: $$20 \times \sin(60^\circ) = 20 \times \frac{\sqrt{3}}{2} = 10\sqrt{3}$$ This matches the given opposite side, confirming the triangle is consistent. 5. **Find adjacent side $x$ using cosine:** $$x = 20 \times \cos(60^\circ)$$ Recall: $$\cos(60^\circ) = \frac{1}{2}$$ So: $$x = 20 \times \frac{1}{2} = 10$$ 6. **Answer:** The length of side $x$ adjacent to the 60° angle is $10$.