1. **State the problem:** We have a right triangle with a base of length 485, angles 28.7° and 40.3°, and we need to find the height $h$ opposite the 40.3° angle. 2. **Identify the relevant formula:** In a right triangle, the height opposite an angle can be found using the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ Here, $h$ is opposite the 40.3° angle, and the hypotenuse is unknown. 3. **Find the hypotenuse:** The base is adjacent to the 28.7° angle, so $$\cos(28.7^\circ) = \frac{485}{\text{hypotenuse}}$$ Rearranged: $$\text{hypotenuse} = \frac{485}{\cos(28.7^\circ)}$$ 4. **Calculate the hypotenuse:** $$\text{hypotenuse} = \frac{485}{\cos(28.7^\circ)}$$ 5. **Find $h$ using sine:** $$h = \sin(40.3^\circ) \times \text{hypotenuse} = \sin(40.3^\circ) \times \frac{485}{\cos(28.7^\circ)}$$ 6. **Simplify and calculate:** $$h = 485 \times \frac{\sin(40.3^\circ)}{\cos(28.7^\circ)}$$ 7. **Evaluate the trigonometric values:** $$\sin(40.3^\circ) \approx 0.647$$ $$\cos(28.7^\circ) \approx 0.877$$ 8. **Calculate $h$ numerically:** $$h \approx 485 \times \frac{0.647}{0.877} = 485 \times 0.738 = 357.93$$ 9. **Round to the nearest integer:** $$h \approx 358$$ **Final answer:** $$\boxed{358}$$