Final answer:
Using the Pythagorean theorem, we calculate the distance from the base of the ladder to the house to be approximately 6.2 feet when the ladder's length is 20 feet and it reaches 19 feet up the side of the house.
Step-by-step explanation:
The student has presented a question involving the application of the Pythagorean theorem to determine the distance from the base of a ladder to the house when the ladder is leaning against the side of a house. Since the ladder is 20 feet long and reaches 19 feet up the side of the house, we can represent this scenario as a right triangle where the ladder is the hypotenuse (20 feet), and one of the legs is the height it reaches on the house (19 feet). The other leg's length, which is the distance from the house to the base of the ladder, can be found by using the Pythagorean theorem:
c^{2} = a^{2} + b^{2}
In this case, c represents the length of the ladder (20 feet), and a represents the vertical reach (19 feet). The length of the base (b) is what we want to find. Plugging in our known values, we get:
20^{2} = 19^{2} + b^{2}
400 = 361 + b^{2}
b^{2} = 400 - 361
b^{2} = 39
b = \sqrt{39}
To the nearest tenth, the distance from the house to the base of the ladder is approximately 6.2 feet.