1. **State the problem:** We need to find the height $h$ of a tree that casts a shadow 10 feet long, with the distance from the top of the tree to the end of the shadow being 26 feet. 2. **Identify the right triangle:** The height of the tree $h$, the shadow length 10 feet, and the hypotenuse 26 feet form a right triangle. 3. **Use the Pythagorean theorem:** For a right triangle, the relationship is $$h^2 + 10^2 = 26^2$$ 4. **Calculate the squares:** $$h^2 + 100 = 676$$ 5. **Isolate $h^2$:** $$h^2 = 676 - 100$$ 6. **Simplify:** $$h^2 = 576$$ 7. **Find $h$ by taking the square root:** $$h = \sqrt{576}$$ 8. **Calculate the square root:** $$h = 24$$ **Final answer:** The height of the tree is 24 feet.