1. **Stating the problem:** We have a tree and a stick casting shadows that meet at point A. The stick has height 3 m (segment BE) and shadow length 5 m (segment AB). The tree's shadow length is 30 m (segment AC), and its height is $h$ (segment CD). We want to find the height $h$ of the tree. 2. **Formula and concept:** Since the stick and the tree cast shadows that meet at the same point A, the triangles formed by the stick and its shadow and the tree and its shadow are similar. 3. **Similarity rule:** For similar triangles, corresponding sides are proportional: $$\frac{\text{height of stick}}{\text{shadow of stick}} = \frac{\text{height of tree}}{\text{shadow of tree}}$$ 4. **Apply values:** $$\frac{3}{5} = \frac{h}{30}$$ 5. **Solve for $h$:** Multiply both sides by 30: $$30 \times \frac{3}{5} = 30 \times \frac{h}{30}$$ Intermediate step with cancellation: $$30 \times \frac{3}{\cancel{5}} = \cancel{30} \times \frac{h}{\cancel{30}}$$ Simplify: $$30 \times \frac{3}{5} = 6 \times 3 = 18$$ So, $$h = 18$$ 6. **Answer:** The height of the tree is $18$ meters.