1. **State the problem:** We are given a trapezoid with an area of 33 square miles, top base length 8 miles, bottom base length 3 miles, and one leg length 8 miles. We need to find the height $h$ of the trapezoid. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times h$$ where $\text{base}_1$ and $\text{base}_2$ are the lengths of the two parallel sides, and $h$ is the height. 3. **Plug in the known values:** $$33 = \frac{(8 + 3)}{2} \times h$$ 4. **Simplify the expression:** $$33 = \frac{11}{2} \times h$$ 5. **Solve for $h$:** Multiply both sides by 2: $$66 = 11h$$ Divide both sides by 11: $$h = \frac{66}{11} = 6$$ 6. **Answer:** The height $h$ of the trapezoid is 6 miles.