Final answer:
To find the distance between the base of the ladder and the wall, we can use the Pythagorean theorem and calculate that it's 16 feet. It is not possible to place a 15-foot ladder at the same 12-foot-high window, 10 feet from the house.
Step-by-step explanation:
A right-angled triangle is formed by the ladder, the wall, and the ground. The ladder is the hypotenuse of the triangle. We can use the Pythagorean theorem to find the distance between the base of the ladder and the wall:
a² + b² = c²
where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse. In this case, a = 12 feet (height of the window) and c = 20 feet (length of the ladder). We want to find b, so we can rearrange the equation:
b² = c² - a²
b² = 20² - 12²
b² = 400 - 144
b² = 256
b = 16 feet
Therefore, the base of the ladder is 16 feet from the wall.
To answer the second question, we can use the same method. Let's assume the base of the ladder is 10 feet from the house. We want to find the length of the ladder that would reach a 12-foot-high window. Using the Pythagorean theorem, we can find that:
b² = c² - a²
b² = 10² - 12²
b² = 100 - 144
b² = -44
Since the length cannot be negative, it is not possible to place a 15-foot ladder at the same 12-feet high window, 10 feet from the house.