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Answer :
Final answer:
Using the Pythagorean theorem, we find that the bottom of the ladder is approximately 22.2 feet from the bottom of the building, corresponding to answer choice A. 22.2 ft.
Explanation:
The student asked how far from the bottom of the building the bottom of the ladder is when a 32-foot ladder leans against the building, touching it at a point 23 feet above the ground. We can solve this problem by using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder serves as the hypotenuse (c = 32 feet), and the height at which the ladder touches the building serves as one of the legs (a = 23 feet). We need to find the distance from the wall (b), which is the other leg:
- a2 + b2 = c2
- 232 + b2 = 322
- b2 = 322 - 232
- b2 = 1024 - 529
- b2 = 495
- b = √495
- b ≈ 22.2 feet
Therefore, the bottom of the ladder is approximately 22.2 feet from the bottom of the building. The closest answer is A. 22.2 ft.
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Rewritten by : Jeany
The distance between bottom of the building from the bottom of the ladder is 22.24 ft.
What is Pythagoras Theorem?
The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Given:
Hypotenuse= 32 foot
Perpendicular= 23 feet
Using Pythagoras theorem
H² = P² + B²
32² = 23² + B²
1024 = 529 + B²
B² = 495
B = 22.24 feet
Hence, the distance between bottom of the building from the bottom of the ladder is 22.24 ft.
Learn more about Pythagoras theorem here:
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