Question
1 A ladder that is 13 feet long leans against a building. The bottom of the ladder is 5 feet away from the base of the building. How far up the side of the building does the ladder reach? feet
Ask by Salazar Stanley. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ladder reaches 12 feet up the side of the building.
Solution
We have a right triangle where the ladder acts as the hypotenuse with a length of 13 feet, the distance from the building is one leg measuring 5 feet, and the height reached on the building is the other leg. According to the Pythagorean theorem:
(hypotenuse)² = (height)² + (base)²
Substituting the known values:
13² = (height)² + 5²
169 = (height)² + 25
Solve for (height)²:
(height)² = 169 - 25
(height)² = 144
Taking the square root of both sides gives:
height = √144
height = 12
Thus, the ladder reaches 12 feet up the side of the building.
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Simplify this solution The Deep Dive
Using the Pythagorean theorem, you can find how high the ladder reaches up the building. This theorem states that in a right triangle, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the height of the building and the distance from the wall). So, we have: \(13^2 = h^2 + 5^2\) Which simplifies to: \(169 = h^2 + 25\) Now subtract 25 from both sides: \(h^2 = 144\) Taking the square root, we find that \(h = 12\) feet. Thus, the ladder reaches 12 feet up the building! And remember, when using ladders, always position them correctly to ensure safety—safety first!
