Final answer:
Using the Pythagorean theorem, we find that the ladder will reach 12 feet high on the house. Gus's ladder, which is 15 feet long, forms a right-angled triangle with the base 9 feet from the house.
Step-by-step explanation:
The student's question relates to the application of the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In Gus's case, the ladder forms a right-angled triangle with the ground and the house. Given that the ladder, which is the hypotenuse, is 15 feet long and the base is 9 feet away from the house, we use the Pythagorean theorem to find the height the ladder will reach:
a² + b² = c²
9² + b² = 15²
81 + b² = 225
b² = 225 - 81
b² = 144
Therefore, b = √144 = 12 feet.
The ladder will reach 12 feet high on the house.