1. The problem states that two right triangles are similar, with Ariadne's height and shadow length given as 5 ft and 15 ft respectively, and Dixon's shadow length as 18 ft. We need to find Dixon's height. 2. Since the triangles are similar, their corresponding sides are proportional. We can set up the proportion: $$\frac{\text{Ariadne's height}}{\text{Ariadne's shadow}} = \frac{\text{Dixon's height}}{\text{Dixon's shadow}}$$ 3. Substitute the known values: $$\frac{5}{15} = \frac{x}{18}$$ where $x$ is Dixon's height. 4. Cross-multiply to solve for $x$: $$5 \times 18 = 15 \times x$$ $$90 = 15x$$ 5. Divide both sides by 15: $$x = \frac{90}{15} = 6$$ 6. Therefore, Dixon is 6 feet tall.