Using math in the real world - Pythagorean theorem

Greenshields23

25 May 202003:15

Summary

TLDRIn this video, Mr. Green-Schultz demonstrates how to use the Pythagorean Theorem to calculate the height of his house. Using a ladder of known length (13 feet), he places it against the house and measures the distance from the base of the ladder to the house (7.75 feet). He illustrates how this creates a right triangle, with the ladder as the hypotenuse. By applying the Pythagorean Theorem (a² + b² = c²), viewers are encouraged to calculate the height of the house. This real-world example shows the practical application of geometry in everyday life.

Takeaways

😀 The speaker uses a ladder to measure the height of their house, as they are too short to measure it directly.
😀 The length of the ladder is determined to be 13 feet.
😀 The speaker places the ladder against the house to form a right triangle.
😀 The situation is modeled as a right triangle, with the ladder as the hypotenuse and the ground distance as one leg.
😀 The speaker uses the Pythagorean theorem to solve for the unknown height of the house.
😀 The ground distance between the house and the base of the ladder is 7 feet 9 inches, or 7.75 feet.
😀 The Pythagorean theorem formula used is: a² + b² = c², where a is the height of the house, b is the ground distance, and c is the length of the ladder.
😀 The speaker asks viewers to solve for the height of the house using the given information.
😀 The correct answer to the height of the house should come from applying the Pythagorean theorem.
😀 This example demonstrates a real-world application of the Pythagorean theorem, where only one side of the triangle is unknown.

Q & A

Why is Mr. Green Schultz using a ladder outside?
-Mr. Green Schultz is using a ladder outside to help measure the height of his house, as he is too short to measure it directly.
How did Mr. Green Schultz measure the ladder?
-Mr. Green Schultz measured the ladder by laying it flat on the ground and determining that it was 13 feet long.
What is the significance of the ladder's length in the problem?
-The length of the ladder, which is 13 feet, serves as the hypotenuse of a right triangle in the Pythagorean theorem to calculate the height of the house.
How does Mr. Green Schultz set up the scenario to calculate the height of his house?
-He places the ladder against the house and imagines a right triangle formed by the ladder, the height of the house, and the distance from the base of the ladder to the house.
What shape is formed when the ladder is placed against the house?
-A right triangle is formed, with the ladder as the hypotenuse, the height of the house as one leg, and the distance from the house to the base of the ladder as the other leg.
What are the measurements needed to apply the Pythagorean theorem?
-The measurements required are the length of the ladder (13 feet) as the hypotenuse, and the distance from the house to the base of the ladder, which is approximately 7 feet 9 inches (or 7.75 feet).
What formula does Mr. Green Schultz use to find the height of his house?
-He uses the Pythagorean theorem: a² + b² = c², where 'a' is the height of the house, 'b' is the distance on the ground (7.75 feet), and 'c' is the length of the ladder (13 feet).
How should the Pythagorean theorem be applied in this scenario?
-The equation becomes a² + 7.75² = 13². By solving for 'a', you can determine the height of the house.
What is the expected outcome after applying the Pythagorean theorem?
-By solving the equation, the height of the house is found to be approximately 12 feet.
Why is this an example of a real-world application of the Pythagorean theorem?
-This is a real-world application because it shows how the Pythagorean theorem can be used to measure something in everyday life, like the height of a house, using simple measurements and basic geometry.