1. **State the problem:** We need to find the height $h$ of a trapezoid with area 48 square miles, top base 6 miles, bottom base 10 miles, and one slanted side 7 miles. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height. 3. **Plug in the known values:** $$48 = \frac{(6 + 10)}{2} \times h$$ 4. **Simplify the expression inside the fraction:** $$48 = \frac{16}{2} \times h$$ 5. **Simplify the fraction:** $$48 = 8 \times h$$ 6. **Solve for $h$ by dividing both sides by 8:** $$h = \frac{48}{8}$$ 7. **Cancel common factors:** $$h = \frac{\cancel{48}}{\cancel{8}} = 6$$ 8. **Final answer:** The height $h$ of the trapezoid is **6 miles**.