1. **State the problem:** Jessica's eyes are 175 cm above the floor. She places a mirror on the ground 650 cm away from a flagpole. She then walks back 1 meter (100 cm) until she sees the top of the flagpole in the mirror. We need to find the height of the flagpole. 2. **Understand the setup:** The mirror on the ground creates two similar right triangles: one formed by Jessica's height and her distance to the mirror, and the other by the flagpole's height and its distance to the mirror. 3. **Identify the triangles:** - Triangle 1 (Jessica's triangle): height = 175 cm, distance to mirror = 650 cm + 100 cm = 750 cm (since she walks back 1 m) - Triangle 2 (Flagpole's triangle): height = unknown $h$, distance to mirror = 650 cm 4. **Use the property of similar triangles:** The ratios of corresponding sides are equal: $$\frac{\text{Jessica's height}}{\text{Jessica's distance}} = \frac{\text{Flagpole's height}}{\text{Flagpole's distance}}$$ 5. **Write the equation:** $$\frac{175}{750} = \frac{h}{650}$$ 6. **Solve for $h$:** $$h = \frac{175}{750} \times 650$$ 7. **Calculate:** $$h = \frac{175 \times 650}{750}$$ 8. **Simplify the fraction:** $$h = \frac{\cancel{175} \times 650}{\cancel{750}} \times \frac{1}{\frac{750}{175}} = \frac{175 \times 650}{750}$$ Calculate numerator and denominator: $$h = \frac{113750}{750}$$ 9. **Divide:** $$h = 151.666\ldots$$ 10. **Round to 1 decimal place:** $$h = 151.7$$ cm **Final answer:** The height of the flagpole is **151.7 cm**.