Pythagorean Theorem Word Problems

Flashcard
•
Mathematics
•
10th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Pythagorean Theorem?
Back
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².
2.
FLASHCARD QUESTION
Front
How do you find the length of one side of a right triangle using the Pythagorean Theorem?
Back
To find the length of one side, rearrange the Pythagorean Theorem formula. For example, to find side a: a = √(c² - b²).
3.
FLASHCARD QUESTION
Front
If a ladder reaches a height of 12 feet and is placed 15 feet away from the wall, how do you find the length of the ladder?
Back
Use the Pythagorean Theorem: c = √(12² + 15²) = √(144 + 225) = √369 ≈ 19.2 feet.
4.
FLASHCARD QUESTION
Front
What is the distance between two points in a coordinate plane?
Back
The distance can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
5.
FLASHCARD QUESTION
Front
In a right triangle, if one leg is 3 units and the other leg is 4 units, what is the length of the hypotenuse?
Back
Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 units.
6.
FLASHCARD QUESTION
Front
How do you solve a word problem involving the Pythagorean Theorem?
Back
Identify the right triangle, assign variables to the sides, apply the Pythagorean Theorem, and solve for the unknown side.
7.
FLASHCARD QUESTION
Front
What is the relationship between the sides of a 30-60-90 triangle?
Back
In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle.
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