1. **State the problem:** We have two similar right triangles, a large one with sides 10, 6, and 11.661904, and a smaller one with sides 2.5, 1.5, and 2.9154759. We need to find the scale factor between the smaller triangle and the larger triangle. 2. **Formula and rules:** The scale factor between two similar triangles is the ratio of any pair of corresponding sides. Since the triangles are similar, the ratios of corresponding sides are equal. 3. **Calculate scale factor using corresponding sides:** - Using the top sides: $$\text{scale factor} = \frac{2.5}{10} = 0.25$$ - Using the right sides: $$\text{scale factor} = \frac{1.5}{6} = 0.25$$ - Using the hypotenuses: $$\text{scale factor} = \frac{2.9154759}{11.661904} \approx 0.25$$ 4. **Confirm consistency:** All three ratios are approximately 0.25, confirming the scale factor. 5. **Final answer:** The scale factor from the large triangle to the small triangle is **0.25**. If you want the scale factor from the small triangle to the large triangle, it is the reciprocal: $$\text{scale factor} = \frac{10}{2.5} = 4$$ or equivalently $$\frac{6}{1.5} = 4$$ or $$\frac{11.661904}{2.9154759} = 4$$ So depending on direction, the scale factor is either 0.25 (small to large) or 4 (large to small). The problem likely asks for the scale factor from the large triangle to the small triangle, which is 0.25. **Rounded to one decimal place:** 0.3