1. **State the problem:** A 20-foot ladder leans against a house reaching 16 feet high. Christian pulls the base 2 feet farther from the house. We need to find the new height the ladder reaches on the house, rounded to the nearest tenth. 2. **Identify the knowns and unknowns:** - Ladder length (hypotenuse) $c = 20$ ft (constant) - Initial height (vertical leg) $a = 16$ ft - Initial base distance (horizontal leg) $b = ?$ - New base distance $b_{new} = b + 2$ - New height $a_{new} = ?$ 3. **Use the Pythagorean theorem:** $$a^2 + b^2 = c^2$$ 4. **Find the initial base distance $b$:** $$b = \sqrt{c^2 - a^2} = \sqrt{20^2 - 16^2} = \sqrt{400 - 256} = \sqrt{144} = 12$$ 5. **Calculate the new base distance:** $$b_{new} = 12 + 2 = 14$$ 6. **Find the new height $a_{new}$ using the Pythagorean theorem:** $$a_{new} = \sqrt{c^2 - b_{new}^2} = \sqrt{20^2 - 14^2} = \sqrt{400 - 196} = \sqrt{204}$$ 7. **Simplify and approximate:** $$a_{new} \approx 14.282856857$$ 8. **Round to the nearest tenth:** $$a_{new} \approx 14.3$$ **Final answer:** The ladder now reaches approximately 14.3 feet up the side of the house.