1. **Problem statement:** A basketball player 2 m tall stands so that the ends of his shadow and the shadow of a pole coincide. The shadow lengths DE and DF are 1.6 m and 4.4 m respectively. We need to find the height of the pole. 2. **Understanding the problem:** The player and the pole cast shadows that end at the same point, so the triangles formed by the player and his shadow and the pole and its shadow are similar. 3. **Formula used:** For similar triangles, corresponding sides are proportional: $$\frac{\text{height of player}}{\text{length of player's shadow}} = \frac{\text{height of pole}}{\text{length of pole's shadow}}$$ 4. **Assign values:** - Height of player = 2 m - Player's shadow length = DE = 1.6 m - Pole's shadow length = DF = 4.4 m - Height of pole = $h$ (unknown) 5. **Set up proportion:** $$\frac{2}{1.6} = \frac{h}{4.4}$$ 6. **Solve for $h$:** Multiply both sides by 4.4: $$h = 4.4 \times \frac{2}{1.6}$$ 7. **Simplify fraction:** $$\frac{2}{1.6} = \frac{2}{\cancel{1.6}} \times \frac{\cancel{1.6}}{1.6} = \frac{2}{1.6} = 1.25$$ 8. **Calculate height:** $$h = 4.4 \times 1.25 = 5.5$$ 9. **Answer:** The pole is approximately 5.5 meters tall.