Final Answer:
The length of the ladder because he Pythagorean theorem helps determine unknown lengths in right-angled triangles, such as finding the length of a ladder against a building. Thus the correct option is 1) The length of the ladder.
Step-by-step explanation:
The Pythagorean theorem provides a way to determine the length of the ladder in a right-angled triangle scenario. Specifically, when the ladder forms the hypotenuse (the side opposite the right angle) and the height of the building and the distance between the ladder and the building form the other two sides of the triangle. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this context, using the Pythagorean theorem, we can find the length of the ladder by knowing the height of the building and the distance between the ladder and the building. By squaring the length of the building's height and the distance from the ladder, summing these squares, and then taking the square root of that sum, we can ascertain the length of the ladder. This mathematical principle is incredibly useful in scenarios involving physical structures like buildings, ladders, and even in various applications across engineering, physics, and everyday problem-solving.
Therefore, when trying to find the unknown length of a ladder leaning against a building, the Pythagorean theorem helps solve for this missing side, making it a crucial tool for measuring heights or distances in real-world situations involving right-angled triangles.
Thus the correct option is 1) The length of the ladder.