1. **State the problem:** We have a 25-foot tall tree and a 10-foot tall fence post. The fence post casts a shadow 22 feet long. We need to find the length of the tree's shadow. 2. **Identify the relationship:** The tree and the fence post form similar triangles with their shadows because the sun's rays create the same angle for both. 3. **Set up the proportion:** Height of tree / Shadow of tree = Height of fence post / Shadow of fence post $$\frac{25}{x} = \frac{10}{22}$$ where $x$ is the length of the tree's shadow. 4. **Solve for $x$:** Cross-multiply: $$25 \times 22 = 10 \times x$$ $$550 = 10x$$ 5. **Divide both sides by 10:** $$\frac{550}{\cancel{10}} = \frac{10x}{\cancel{10}}$$ $$55 = x$$ 6. **Conclusion:** The tree's shadow is 55 feet long.