Final answer:
Jill's ladder, which is 10 feet long and placed 4 feet away from the house, reaches approximately 9.17 feet up the side of the house, as calculated using the Pythagorean theorem.
Step-by-step explanation:
The question involves determining how high Jill's ladder reaches up on the side of the house using the length of the ladder and the distance from the base to the house.
This is a classic right-triangle problem, where we can apply the Pythagorean theorem to find the missing side. The ladder forms the hypotenuse of the triangle, the distance from the house is one leg, and the height up the house is the other.
The formula of the Pythagorean theorem is a2 + b2 = c2, where 'c' is the hypotenuse and 'a' and 'b' are the other two sides. Given that the ladder is 10 feet long (hypotenuse) and the distance from the base of the house to the bottom of the ladder is 4 feet (one of the legs), we can set up the equation as:
Let 'h' be the height the ladder reaches up the side of the house.
Then, 42 + h2 = 102.
We solve for 'h': 16 + h2 = 100.
Subtract 16 from both sides: h2 = 84.
Take the square root of both sides: h = √84 ≈ 9.17 feet.
Therefore, Jill's ladder reaches approximately 9.17 feet up the side of the house.