1. **State the problem:** A girl 160 cm tall stands 360 cm from a lamp post. Her shadow is 90 cm long. We need to find the height of the lamp post. 2. **Use the concept of similar triangles:** The lamp post, the girl, and their shadows form two similar right triangles. The ratio of height to shadow length is the same for both. 3. **Set up the proportion:** Let the height of the lamp post be $h$ cm. $$\frac{h}{360 + 90} = \frac{160}{90}$$ Note: The lamp post's shadow length is the distance from the lamp post to the tip of the girl's shadow, which is $360 + 90 = 450$ cm. 4. **Solve for $h$:** $$h = \frac{160}{90} \times 450$$ 5. **Calculate:** $$h = \frac{160}{90} \times 450 = \cancel{\frac{160}{\cancel{90}}} \times \cancel{\frac{450}{5}} = \frac{160}{1} \times 5 = 800$$ 6. **Answer:** The lamp post is 800 cm tall.