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

我懂了，正弦是对比斜。是的。

You know, cosine is adjacent over hypotenuse.

你们知道 cos是邻除以斜。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只是两长度为 1 的 直角三角形之斜。

Opposite over hypotenuse is equal to sine of an angle.

斜分之对 的即是 sin 函数的。

So you have the opposite over the hypotenuse.

是对比斜。

Arrange them so that their hypotenuses form a tilted square.

将它们排列起来，使其斜形成一个倾斜的正方形。

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，斜长 c。

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

是因为个向量，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是直角三角形的和斜之间的关系。

What involves the hypotenuse and the opposite side?

什么涉及斜和对？

After the hymn, the teacher taught students the hypotenuse.

赞美诗后，老师教学生直角三角形的斜。

So what involves the opposite and the hypotenuse?

那么什么涉及对立面和斜呢？

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

它在斜上相邻。那是 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.

斜平方等于直角平方和把我给惊呆了。

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

表明直角三角形各的平方加起来等于其斜的平方。

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.

他们都对毕达哥拉斯定（勾股定）做出了精彩的证明；个定是说，对于一个直角三角形，一的平方加上另一的平方等于斜的平方。

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提出了优雅的证明，条规则说对于直角三角形，一侧的平方加上另一侧的平方等于斜的平方。