Final answer:
Using the Pythagorean theorem, it is determined that the base of a 14-foot ladder, which is leaning against a building and reaches 9.8 ft up the wall, is approximately 10 feet from the building.
Step-by-step explanation:
To determine how far the base of the ladder is from the building, we can apply the Pythagorean theorem to this right triangle problem. The ladder represents the hypotenuse of the right triangle, the height the ladder reaches on the wall is one leg, and the distance from the building to the base of the ladder is the other leg.
Given that A 14-foot ladder is leaning against the side of a building and the ladder reaches 9.8 ft up the wall, we can denote the length of the ladder (the hypotenuse) as 'c' which is 14 ft, and the distance up the wall (one leg of the triangle) as 'a' which is 9.8 ft. We are looking to find 'b', the length of the other leg of the triangle which represents the distance from the building to the base of the ladder.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we plug in our known values:
So our equation to solve for 'b' (the base) is:
- 9.8^2 + b^2 = 14^2
- b^2 = 14^2 - 9.8^2
- b^2 = 196 - 96.04
- b^2 = 99.96
- b = √99.96
- b ≈ 10 feet
Hence, the base of the ladder is approximately 10 feet from the building.