1. **State the problem:** We know the height of a tree and the length of its shadow are directly proportional. 2. **Given data:** - Tree 1 height $h_1 = 12$ m - Tree 1 shadow length $s_1 = 8$ m - Tree 2 shadow length $s_2 = 13.8$ m - Tree 2 height $h_2 = ?$ 3. **Set up the proportion:** Since height and shadow length are directly proportional, we have $$\frac{h_1}{s_1} = \frac{h_2}{s_2}$$ 4. **Substitute known values:** $$\frac{12}{8} = \frac{h_2}{13.8}$$ 5. **Solve for $h_2$:** $$h_2 = \frac{12}{8} \times 13.8 = 1.5 \times 13.8 = 20.7$$ 6. **Interpretation:** The height of the tree with a 13.8 m shadow is $20.7$ meters. **Final answer:** $20.7$ m