1. **State the problem:** We need to find how much higher the longer brace reaches compared to the shorter brace. 2. **Recall given data:** - Shorter brace length $= 8$ m at $45^\circ$ angle to the house side. - Longer brace length $= 11.3$ m at $30^\circ$ angle to the house side. 3. **Find the height each brace reaches:** The height reached by a brace is the vertical component of its length, calculated by multiplying the length by the cosine of the angle it makes with the vertical side of the house. 4. **Calculate height of shorter brace:** $$\text{Height}_{short} = 8 \times \cos 45^\circ = 8 \times \frac{\sqrt{2}}{2} = 8 \times 0.7071 = 5.6568 \approx 5.7 \text{ m}$$ 5. **Calculate height of longer brace:** $$\text{Height}_{long} = 11.3 \times \cos 30^\circ = 11.3 \times \frac{\sqrt{3}}{2} = 11.3 \times 0.8660 = 9.7858 \approx 9.8 \text{ m}$$ 6. **Find the difference in height:** $$\text{Difference} = \text{Height}_{long} - \text{Height}_{short} = 9.8 - 5.7 = 4.1 \text{ m}$$ **Final answer:** The longer brace reaches approximately 4.1 m higher than the shorter brace.