1. **Problem:** Find the values of $x$ and $y$ in the first triangle where the hypotenuse is 20 and the angle opposite side $y$ is 30°. 2. **Formula and rules:** In a 30°-60°-90° right triangle, the sides are in the ratio: $$\text{opposite }30^\circ : \text{opposite }60^\circ : \text{hypotenuse} = 1 : \sqrt{3} : 2$$ This means: - The side opposite 30° is half the hypotenuse. - The side opposite 60° is $\sqrt{3}$ times the side opposite 30°. 3. **Apply the formula:** - Hypotenuse $= 20$ - Side opposite 30° is $x$ (unknown) - Side adjacent to 30° is $y$ (unknown) 4. **Calculate $x$:** $$x = \frac{1}{2} \times 20 = 10$$ 5. **Calculate $y$:** $$y = x \times \sqrt{3} = 10 \sqrt{3}$$ 6. **Answer:** $$x = 10, \quad y = 10 \sqrt{3}$$ This completes the solution for the first triangle.