1. **State the problem:** We have two similar triangles ABC and EBD with sides AB = 9 ft, AC = h, DE = 7 ft, and BE = 15 ft. We need to find the unknown side length $h$. 2. **Formula and rules:** For similar triangles, corresponding sides are proportional. This means: $$\frac{AB}{DE} = \frac{AC}{BE}$$ 3. **Set up the proportion:** $$\frac{9}{7} = \frac{h}{15}$$ 4. **Solve for $h$:** Cross multiply: $$9 \times 15 = 7 \times h$$ $$135 = 7h$$ Divide both sides by 7: $$\frac{135}{\cancel{7}} = \frac{7h}{\cancel{7}}$$ $$h = \frac{135}{7}$$ 5. **Simplify the fraction:** $$h \approx 19.29$$ ft **Answer:** The unknown side length $h$ is approximately 19.29 ft.