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

我懂了，正弦是对边比斜边。是的。

You know, cosine is adjacent over hypotenuse.

你们知道 cos是邻边除以斜边。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只是两边长度为 1 的 直角三角形之斜边。

Opposite over hypotenuse is equal to sine of an angle.

斜边分之对边 的值即是 sin 函数的值。

So you have the opposite over the hypotenuse.

这里是对边比斜边。

Arrange them so that their hypotenuses form a tilted square.

将它们排列起来，使其斜边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，两边分别长 a 和 b，斜边长 c。

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

这是因为这个向量，让它的量值当分母。

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边和斜边之间的关系。

What involves the hypotenuse and the opposite side?

什么涉及斜边和对边？

After the hymn, the teacher taught students the hypotenuse.

赞美诗后，老师教学生直角三角形的斜边。

So what involves the opposite and the hypotenuse?

那么什么涉及对立面和斜边呢？

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

它在斜边上相邻。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的平方加起来等于其斜边的平方。

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理（勾股定理）做出了精彩的证明；这个定理是说，对于一个直角三角形，一边的平方加上另一边的平方等于斜边的平方。

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，这条规则说对于直角三角形，一侧的平方加上另一侧的平方等于斜边的平方。