ok ok, I found my answer on my own thanks again for your attention...fresh_42 said:Did you mean this?
https://en.wikipedia.org/wiki/Law_of_cosines#Proofs
Or what is its generalized form?
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Pythagoras theorem can be generalized to any polygon, not just right triangles. This is done by using the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those two sides multiplied by the cosine of the angle between them.
Generalizing Pythagoras theorem allows us to apply the concept to a wider range of shapes and scenarios, making it a more versatile and useful tool in mathematics and science. It also helps to deepen our understanding of the fundamental principles behind the theorem.
The generalized Pythagoras theorem is used in fields such as engineering, architecture, and navigation. For example, it can be used to calculate the distance between two points on a map, the height of a building, or the tension in a bridge's support cables.
The generalized Pythagoras theorem can be proven using various methods, including algebraic proofs, geometric proofs, and trigonometric proofs. These proofs involve manipulating equations and geometric figures to show that the theorem holds true for any polygon.