1. **State the problem:** We are given that triangles $\triangle ABC$ and $\triangle EDC$ are similar, and we need to find the distance $x$ across the bay, which corresponds to side $AB$ in $\triangle ABC$. Given sides are $ED = 18.0$ m, $DC = 15.0$ m, and $BC = 30.0$ m. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{AB}{ED} = \frac{BC}{DC}$$ 3. **Set up the proportion:** $$\frac{x}{18} = \frac{30}{15}$$ 4. **Simplify the right side:** $$\frac{30}{15} = 2$$ 5. **Solve for $x$:** $$x = 18 \times 2 = 36$$ 6. **Final answer:** The distance $x$ across the bay is $36$ meters.