Final answer:
The length of the ladder is calculated using the Pythagorean theorem, and the closest length to our calculated value from the given choices is 20 feet.
Step-by-step explanation:
Mr. Roosevelt is leaning a ladder against the side of his son's treehouse to repair the roof. The top of the ladder reaches the roof, which is 18 feet from the ground, and the base of the ladder is 5 feet away from the tree. To determine the length of the ladder, we can use the Pythagorean theorem since the ladder, ground, and the height of the treehouse form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². Here, a is the height of the treehouse (18 feet), and b is the distance from the tree to the ladder base (5 feet).
Calculating this we get:
18² + 5² = c²
324 + 25 = c²
349 = c²
√c² = √349
c ≈ 18.68 feet
Since the question provides us with multiple choices, we can see that the closest length to our calculated value is 20 feet (answer C).