1. **State the problem:** We have two poles. Pole 1 is 6.5 feet tall. The distance between the poles is 8 feet, and the line from the top of pole 1 to the top of pole 2 is angled 15 degrees downward from the horizontal. We want to find the height of pole 2. 2. **Formula and explanation:** The vertical height difference between the poles can be found using trigonometry. The vertical drop $h$ is given by: $$h = d \times \tan(\theta)$$ where $d=8$ feet is the horizontal distance and $\theta=15^\circ$ is the angle downward. 3. **Calculate the vertical drop:** $$h = 8 \times \tan(15^\circ)$$ Using $\tan(15^\circ) \approx 0.2679$: $$h = 8 \times 0.2679 = 2.1432$$ 4. **Find the height of pole 2:** Since pole 2 is lower by this vertical drop: $$\text{Height of pole 2} = 6.5 - 2.1432 = 4.3568$$ 5. **Final answer:** The height of pole 2 is approximately $$\boxed{4.36 \text{ feet}}$$