1. **State the problem:** We want to find how high the drawbridge rises when the angle $x$ is $30^\circ$, $45^\circ$, and $60^\circ$. The drawbridge half is the hypotenuse of a right triangle with length 284 feet. 2. **Formula used:** In a right triangle, the height opposite angle $x$ can be found using the sine function: $$\text{height} = \text{hypotenuse} \times \sin(x)$$ 3. **Calculate height for each angle:** - For $x=30^\circ$: $$\text{height} = 284 \times \sin(30^\circ)$$ $$= 284 \times \frac{1}{2}$$ $$= 142$$ - For $x=45^\circ$: $$\text{height} = 284 \times \sin(45^\circ)$$ $$= 284 \times \frac{\sqrt{2}}{2}$$ $$= 284 \times 0.7071 \approx 200.7$$ - For $x=60^\circ$: $$\text{height} = 284 \times \sin(60^\circ)$$ $$= 284 \times \frac{\sqrt{3}}{2}$$ $$= 284 \times 0.8660 \approx 245.9$$ 4. **Final answers:** - Height at $30^\circ$ is 142 feet. - Height at $45^\circ$ is approximately 200.7 feet. - Height at $60^\circ$ is approximately 245.9 feet. This means the drawbridge rises higher as the angle increases, following the sine function relationship.