1. **State the problem:** We have a right triangle with a right angle at the bottom right vertex, a 30° angle at the top vertex, and sides labeled as follows: the hypotenuse is 16, the side opposite the 30° angle is $y$, and the side adjacent to the 30° angle is $x$. We need to find $x$ and $y$ rounded to two decimal places. 2. **Recall the relevant formulas:** In a right triangle, the side lengths relate to the angles by the sine and cosine functions: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ For $\theta = 30^\circ$: $$y = 16 \times \sin(30^\circ), \quad x = 16 \times \cos(30^\circ)$$ 3. **Calculate $y$:** $$y = 16 \times \sin(30^\circ) = 16 \times 0.5 = 8$$ 4. **Calculate $x$:** $$x = 16 \times \cos(30^\circ) = 16 \times \frac{\sqrt{3}}{2} = 16 \times 0.8660254038$$ 5. **Simplify $x$:** $$x = 16 \times 0.8660254038 = 13.85640646$$ Rounded to two decimal places: $$x \approx 13.86$$ 6. **Final answers:** $$x = 13.86, \quad y = 8.00$$