Pythagorean Theorem: Finding the Distance of a Ladder's Base from the House

Question:

A 12 ft. ladder leans against the house. The house is 10 ft. How far is the base of the ladder from the house? Round your answer to the nearest tenth.

a) 6.6 ft
b) 7.2 ft
c) 8.2 ft
d) 9.6 ft

Final Answer:

To find the distance from the base of the ladder to the house, one must use the Pythagorean theorem. The calculation shows that the ladder's base is roughly 6.6 ft from the house, so the answer is (a) 6.6 ft.

Explanation: The question involves determining the distance from the base of a ladder to the house given the length of the ladder and the height at which it leans against the house. This problem can be solved using the Pythagorean theorem which states that in a right 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. In this scenario, the ladder represents the hypotenuse of a right-angled triangle, the height of the house is one of the sides, and we need to calculate the length of the other side, which is the distance from the base of the ladder to the house.

Ladder length (hypotenuse) = 12 ft
Height of the house (one side) = 10 ft
Required to find: Distance of the ladder's base from the house (other side)

Using the Pythagorean theorem:
a² + b² = c²
b² = c² - a²
b² = 12² - 10²
b² = 144 - 100
b² = 44
b = √44
b ≈ 6.6 ft

The base of the ladder is approximately 6.6 ft from the house. Therefore, the correct answer is (a) 6.6 ft.