1. **State the problem:** We need to find the height of the flagpole, which is the vertical leg of a right triangle. 2. **Identify the known sides:** The horizontal leg is 10 ft, the hypotenuse is 26 ft, and the vertical leg (height) is unknown. 3. **Use the Pythagorean theorem:** For a right triangle, $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 4. **Assign values:** Let the height be $h$. Then: $$10^2 + h^2 = 26^2$$ 5. **Calculate squares:** $$100 + h^2 = 676$$ 6. **Isolate $h^2$:** $$h^2 = 676 - 100$$ $$h^2 = 576$$ 7. **Take the square root:** $$h = \sqrt{576}$$ 8. **Simplify:** $$h = 24$$ **Answer:** The height of the flagpole is 24 ft.