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

我懂了，弦对边比边。。

You know, cosine is adjacent over hypotenuse.

你们 cos邻边除以边。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只两边长度为 1 直角三角形之边。

Opposite over hypotenuse is equal to sine of an angle.

边分之对边 即 sin 函数。

So you have the opposite over the hypotenuse.

这里对边比边。

Arrange them so that their hypotenuses form a tilted square.

将它们排列起来，使其边形成一个倾方形。

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

取四个全等直角三角形，两边分别长 a 和 b，边长 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.

几何中最著名关系直角三角形边和边之间关系。

What involves the hypotenuse and the opposite side?

什么涉及边和对边？

After the hymn, the teacher taught students the hypotenuse.

赞美诗后，老师教学生直角三角形边。

So what involves the opposite and the hypotenuse?

那么什么涉及对立面和边呢？

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

它在边上相邻。那 3 除 2 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.

边平方等于直角边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边平方加起来等于其边平方。

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.

他们都对毕达哥拉斯定理（勾股定理）做出了精彩证明；这个定理说，对于一个直角三角形，一边平方加上另一边平方等于边平方。

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.

他们都为著名毕达哥拉斯定理提出了优雅证明，这条规则说对于直角三角形，一侧平方加上另一侧平方等于边平方。