3D Applications of Pythagorean Theorem Warmup

Flashcard
•
Mathematics
•
8th Grade
•
Hard
+2
Standards-aligned
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14 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.
Tags
CCSS.8.G.B.8
2.
FLASHCARD QUESTION
Front
How do you calculate the length of a ladder leaning against a wall?
Back
Use the Pythagorean Theorem. If the height from the ground to the point where the ladder touches the wall is 'a' and the distance from the wall to the base of the ladder is 'b', then the length of the ladder 'c' can be calculated as: c = √(a² + b²).
Tags
CCSS.8.G.B.8
3.
FLASHCARD QUESTION
Front
If a ladder reaches 12 feet high and is placed 9 feet from the wall, what is the length of the ladder?
Back
Using the Pythagorean Theorem: c = √(12² + 9²) = √(144 + 81) = √225 = 15 feet.
Tags
CCSS.8.G.B.8
4.
FLASHCARD QUESTION
Front
What is the diagonal length of a rectangle with sides 6 inches and 8 inches?
Back
Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 inches.
Tags
CCSS.8.G.B.8
5.
FLASHCARD QUESTION
Front
In 3D modeling, why is the Pythagorean Theorem important?
Back
It is used to measure distances between objects, calculate texture dimensions, and determine the correct scale of models, ensuring accuracy in virtual environments.
Tags
CCSS.8.G.B.8
6.
FLASHCARD QUESTION
Front
What is the distance from the base of a house to place a 15' ladder to reach a 12' wall?
Back
Using the Pythagorean Theorem: b = √(15² - 12²) = √(225 - 144) = √81 = 9 feet.
Tags
CCSS.8.G.B.8
7.
FLASHCARD QUESTION
Front
What is the formula for finding the distance between two points in 3D space?
Back
The distance formula in 3D is: d = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).
Tags
CCSS.HSG.GPE.B.7
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