1. **State the problem:** We need to find the distance $x$ between two poles connected by a wire of length 80 ft, where the wire forms a 20° angle with the horizontal. 2. **Identify the triangle and formula:** The wire is the hypotenuse of a right triangle, the angle adjacent to $x$ is 20°, and $x$ is the base (adjacent side). 3. **Use trigonometry:** The cosine of an angle in a right triangle is the ratio of the adjacent side over the hypotenuse: $$\cos(20^\circ) = \frac{x}{80}$$ 4. **Solve for $x$:** $$x = 80 \times \cos(20^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\cos(20^\circ) \approx 0.9397$$ So, $$x \approx 80 \times 0.9397 = 75.176$$ 6. **Final answer:** The distance between the two poles is approximately $$\boxed{75.18 \text{ ft}}$$