1. **State the problem:** We have a flagpole casting a 6 m shadow and a 2 m tall post casting a 1.5 m shadow at the same time. We want to find the height $h$ of the flagpole using similar triangles. 2. **Set up the similarity ratio:** Since the sun's rays create similar right triangles, the ratio of height to shadow length for the post should equal that of the flagpole: $$\frac{2}{1.5} = \frac{h}{6}$$ 3. **Solve for $h$ using Student A's proportion:** Multiply both sides by 6: $$6 \times \frac{2}{1.5} = h$$ Simplify the fraction: $$\frac{2}{1.5} = \frac{2}{\cancel{1.5}} \times \frac{\cancel{1.5}}{1.5} = \frac{2}{1.5} = \frac{4}{3}$$ So, $$h = 6 \times \frac{4}{3} = 8$$ 4. **Check Student B's proportion:** Student B set up: $$\frac{1.5}{2} = \frac{6}{h}$$ Cross-multiplied: $$1.5h = 12$$ Solve for $h$: $$h = \frac{12}{1.5} = 8$$ 5. **Evaluate Student B's conclusion:** Student B concluded $h=4$ which is incorrect because the proportion was set up incorrectly. The ratio of height to shadow length must be consistent, so the numerator and denominator must correspond correctly. 6. **Conclusion:** Student A is correct; Student B set up an incorrect proportion. **Final answer:** C. Student A is correct; Student B set up an incorrect proportion.