1. **State the problem:** We have two poles. Pole 1 is 6 feet tall. The distance between the poles is 8 feet, and the angle of elevation from the top of pole 1 to the top of pole 2 is 15 degrees. We need to find the height of pole 2. 2. **Formula and explanation:** We can model this as a right triangle where the horizontal distance between the poles is 8 feet, the vertical difference in height is unknown, and the angle of elevation is 15 degrees. We use the tangent function, which relates the angle to the opposite side (height difference) and adjacent side (distance): $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 15^\circ$, opposite = height difference between poles, adjacent = 8 feet. 3. **Calculate height difference:** $$\tan(15^\circ) = \frac{h_2 - 6}{8}$$ Multiply both sides by 8: $$8 \times \tan(15^\circ) = h_2 - 6$$ 4. **Solve for $h_2$:** $$h_2 = 6 + 8 \times \tan(15^\circ)$$ 5. **Evaluate $\tan(15^\circ)$:** Using a calculator, $\tan(15^\circ) \approx 0.2679$ 6. **Calculate:** $$h_2 = 6 + 8 \times 0.2679 = 6 + 2.1432 = 8.1432$$ 7. **Final answer:** The height of pole 2 is approximately **8.14 feet**.