You know, cosine is adjacent over hypotenuse.

你们知道 cos是邻边除以斜边。

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。

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

我懂了，正弦是对边比斜边。是的。

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

斜边平直角边平和可把我给惊呆了。

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）做出了彩的证明；这个定理是说，对一个直角三角形，一边的平加上另一边的平斜边的平。

So that was just one side of each of the trapezoid notches.

刚才只裁切好了梯形卡槽的单侧斜边。

If that's true, then the slopes of their diagonal sides should be the same.

如果这是真的， 他们斜边的斜率 就应该是一样的。

That the x component is going to be the cosine of the angle between the hypotenuse and the x component times the hypotenuse.

这个x分量应该於乘以斜边所以同样的 这里的x分量。

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。

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

取四个全的直角三角形，两边分别长 a 和 b，斜边长 c。

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形。

So the magnitude of this over the hypotenuse of this right triangle.

直角三角形的斜边是多少 直角三角形的斜边是多少。

And you could do your SOH-CAH-TOA.

你们知道 cos是邻边除以斜边。

I think he knew what a hypotenuse was when he was about five.

我想他大概五岁就知道什么是斜边了。

Well, it's ambling its way along a hypotenuse, along a slopey angle.

好吧，它正沿着斜边，沿着一个倾斜的角度慢慢前行。

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.

他们都为着名的勾股定理提出了简洁的证明，该定理指出， 对一个直角三角形，一条直角边的平加上另一条直角边的平斜边的平。

Yonder, for example, is Cathedral Peak, some three miles away, with a scattered growth of this pine creeping like mosses over the roof and around the beveled edges of the north gable, nowhere giving any hint of an ascending axis.

例如，远处是大教堂峰，大约三英里外，这棵松树零星地生长，像苔藓一样爬过屋顶和北山墙的斜边，没有任何迹象表明有上升的轴。

And so what they thought, and this is what the ancient historians described, is that they effectively tried to draw a right angle triangle with the two entrances at each end of the hypotenuse.

他们认为， 古代历史学家描述的就是，他们实际上试图画一个直角三角形， 两个入口分别位斜边的两端。

To think about the projection, let's make a little right triangle like this, where what was the height of our spherical rectangle is the hypotenuse, and its projection is one of the legs.

要想考虑投影， 我们可以画一个小直角三角形，其中球面矩形的高度是斜边，其投影是其中一个直角边。

So 9 squared, which is 81 plus 81, so to figure out what that hypotenuse is, it is the square root of 162 or it is around 12.7.

所以9的平是81， 再加上81，因此斜边的长度就是162的平根， 大约是12.7。