1. Problem 14: Given a right triangle with a 30° angle and sides labeled $m$, $n$, and 16, find the correct values of $m$ and $n$. 2. Recall the properties of a 30°-60°-90° triangle: the side opposite 30° is half the hypotenuse, and the side opposite 60° is $\sqrt{3}$ times the side opposite 30°. 3. Since the triangle has a right angle and a 30° angle, the hypotenuse is the side opposite the right angle, which is 16. 4. Calculate the side opposite 30°: $n = \frac{16}{2} = 8$. 5. Calculate the side opposite 60°: $m = 8 \times \sqrt{3} = 8\sqrt{3}$. 6. Therefore, the correct values are $m = 8\sqrt{3}$ and $n = 8$, which corresponds to option C. 7. Problem 15: Given a right triangle with a 60° angle and sides labeled $x$, $y$, and 3, find the correct values of $x$ and $y$. 8. Recall the properties of a 30°-60°-90° triangle: the side opposite 30° is half the hypotenuse, and the side opposite 60° is $\sqrt{3}$ times the side opposite 30°. 9. The hypotenuse is 3. 10. The side opposite 30° is $x = \frac{3}{2} = 1.5$. 11. The side opposite 60° is $y = x \times \sqrt{3} = \frac{3}{2} \times \sqrt{3} = \frac{3\sqrt{3}}{2}$. 12. Therefore, the correct values are $x = \frac{3}{2}$ and $y = \frac{3\sqrt{3}}{2}$, which corresponds to option D.