>>20459

A "cosine" of an angle in a triangle is the ratio of two specific sides in relation to that angle. Any two triangles whose three angles are the same will also have proportionally identical side lengths, so the ratio of any two of their sides relative to a specific angle will be the same across those two triangles. This means that the cosine of any particular angle will always be the same, regardless of which triangle it appears in.

The Law of Cosines is a formula that involves the cosine of an angle. Given a triangle with sides of length a, b, and c; and the angle between sides a and b measuring γ; the Law is commonly stated c² = a² + b² - 2ab・cos(γ) . Using this formula, you can compute the length of one of the sides if you know the length of the two other sides and the angle between them, or you can compute the angles of the triangle if you know the lengths of all three sides.

Notice that cos(90°) = 0. So if γ = 90°, then 2ab・cos(γ) = 2ab・0 = 0. Inserting this value into the Law of Cosines, it becomes c² = a² + b², a popular geometric formula generally known as the Pythagorean Theorem. Given this, you can see the Law of Cosines as a sort of generalized Pythagorean Theorem: it allows you to compute some properties of a triangle if you know other properties of it.

I hope that clears up your confusion. I hope your statement of confusion wasn't a joke. I couldn't be sure, given the context.