I get it! Sin is opposite hypotenuse... Yes.

我懂了，正弦比。的。

You know, cosine is adjacent over hypotenuse.

你们知道 cos邻除以。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只两长度为 1 的 直角三角形。

Opposite over hypotenuse is equal to sine of an angle.

分 的即 sin 函数的。

So you have the opposite over the hypotenuse.

这比。

Arrange them so that their hypotenuses form a tilted square.

将它们排列起来，使其形成一个倾的正方形。

Take four identical right triangles with side lengths a and b and hypotenuse length c.

取四个全等的直角三角形，两分别长 a 和 b，长 c。

And this comes straight out of this magnitude, which is opposite to the angle over the hypotenuse.

这因为这个向量，让它的量当分母。

The most famous relation in geometry is the relation between the sides and the hypotenuse of a right triangle.

几何中最著名的关系直角三角形的和间的关系。

What involves the hypotenuse and the opposite side?

什么涉及和？

After the hymn, the teacher taught students the hypotenuse.

赞美诗后，老师教学生直角三角形的。

So what involves the opposite and the hypotenuse?

那么什么涉及立面和呢？

It's adjacent over hypotenuse. And that's square root of 3 over 2.

它在上相邻。那 3 除 2 的平方根。

You know, I was blown away that the square of the hypotenuse was the sum of the squares of the opposite sides.

平方等于直角平方和可把我给惊呆了。

That states that the squares of the sides of a right triangle add up to the square of its hypotenuse.

这表明直角三角形各的平方加起来等于其的平方。

They all came up with elegant proofs for the famous Pythagorean theorem; the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都毕达哥拉斯定理（勾股定理）做出了精彩的证明；这个定理说，于一个直角三角形，一的平方加上另一的平方等于的平方。

They all came up with elegant proofs for the famous Pythagorean theorem, the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都为著名的毕达哥拉斯定理提出了优雅的证明，这条规则说于直角三角形，一侧的平方加上另一侧的平方等于的平方。