Exploring 3D Applications of the Pythagorean Theorem

The video tutorial explains how to apply the Pythagorean theorem to 3D objects, using several examples to demonstrate the process. It begins with a scenario involving a candle and a box, showing how to determine if the candle fits diagonally. Subsequent examples involve calculating missing lengths in right triangles and solving more complex triangle problems. The tutorial concludes with finding the length of a specific line segment using given dimensions.

What theorem is used to solve the problem of fitting the candle in the box?

• Quantum mechanics

• Thermodynamics

• Theory of relativity

• Pythagorean theorem

What is the height of the candle mentioned?

• 6 inches

• 7 inches

• 8 inches

• 5 inches

How is the Pythagorean theorem formula written?

• a^2 - b^2 = c^2

• a^2 / b^2 = c^2

• a^2 + b^2 = c^2

• a^2 * b^2 = c^2

What are the dimensions of the base of the box?

• 5 inches by 6 inches

• 6 inches by 7 inches

• 4 inches by 5 inches

• 3 inches by 4 inches

What is the length of the diagonal of the box's base?

• 7 inches

• 6 inches

• 5 inches

• 8 inches

What is the final length of the diagonal where the candle fits?

• 8.6 inches

• 9 inches

• 7.5 inches

• 8 inches

What are the dimensions used to find the hypotenuse in the second example?

• 5 inches and 12 inches

• 7 inches and 14 inches

• 6 inches and 13 inches

• 4 inches and 11 inches

What is the length of the hypotenuse found in the third example?

• 23.8 inches

• 24.5 inches

• 25.3 inches

• 26 inches

In the final example, what is the length of AC?

• 12 centimeters

• 13 centimeters

• 14 centimeters

• 15 centimeters

What is the final length found in the last example?

• 12.8 centimeters

• 13.2 centimeters

• 13.5 centimeters

• 14 centimeters