1. **State the problem:** We have a right triangle with a hypotenuse of length 29 inches and a vertical side (height) of 14 inches. We need to find the length of the horizontal side (base). 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the legs of the triangle. 3. **Assign values:** Let the base be $x$. Then: $$x^2 + 14^2 = 29^2$$ 4. **Calculate squares:** $$x^2 + 196 = 841$$ 5. **Isolate $x^2$:** $$x^2 = 841 - 196$$ $$x^2 = 645$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{645}$$ 7. **Simplify the square root if possible:** $$645 = 3 \times 5 \times 43$$ No perfect square factors other than 1, so: $$x = \sqrt{645} \approx 25.4$$ **Final answer:** The horizontal distance (base) is approximately $25.4$ inches.