1. **Problem statement:** We have a mountain pass with a 45° steep slope going up for 2.8 km, and then an equally steep 45° slope going down on the other side. The start and end points are at the same height. We need to find the length of the downhill slope. 2. **Understanding the problem:** Since both slopes are at 45° and the start and end points are at the same height, the uphill and downhill slopes form two equal angles with the horizontal, and the vertical height gained going up equals the vertical height lost going down. 3. **Formula and approach:** For a slope at angle $\theta$ with length $L$, the vertical height $h$ is given by: $$h = L \sin(\theta)$$ Since the uphill length is 2.8 km and $\theta = 45^\circ$, the vertical height is: $$h = 2.8 \times \sin(45^\circ)$$ The downhill slope length $x$ satisfies: $$h = x \times \sin(45^\circ)$$ Because the vertical heights are equal, we have: $$2.8 \times \sin(45^\circ) = x \times \sin(45^\circ)$$ 4. **Simplify and solve for $x$:** $$\cancel{\sin(45^\circ)} \times 2.8 = x \times \cancel{\sin(45^\circ)}$$ $$2.8 = x$$ 5. **Answer:** The downhill slope length is also 2.8 km. This makes sense because the slopes are symmetric and the start and end points are at the same height.