1. **State the problem:** We have a stick 0.5 m high casting a shadow 1.25 m long, and a tree casting a shadow 10 m long. We need to find the height of the tree using similar triangles. 2. **Formula and concept:** When two triangles are similar, their corresponding sides are proportional. So, the ratio of the height to the shadow length of the stick equals the ratio of the height to the shadow length of the tree. 3. **Set up the proportion:** $$\frac{\text{height of stick}}{\text{shadow of stick}} = \frac{\text{height of tree}}{\text{shadow of tree}}$$ 4. **Substitute known values:** $$\frac{0.5}{1.25} = \frac{h}{10}$$ 5. **Solve for $h$ (height of the tree):** Multiply both sides by 10: $$10 \times \frac{0.5}{1.25} = h$$ 6. **Simplify the fraction:** $$\frac{0.5}{1.25} = \frac{\cancel{0.5}}{\cancel{1.25}} = \frac{1}{2.5}$$ 7. **Calculate $h$:** $$h = 10 \times \frac{1}{2.5} = \frac{10}{2.5}$$ 8. **Simplify division:** $$h = \frac{\cancel{10}}{\cancel{2.5}} = 4$$ 9. **Final answer:** The height of the tree is **4 meters**.