You know, cosine is adjacent over hypotenuse.

你们知道 cos是邻除以。

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

几何中最著名关系是直角三角形和之间关系。

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

我懂了，正弦是对。是。

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。

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）做出了彩证明；这个定理是说，对于一个直角三角形，一平方加上另一平方等于平方。

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

刚才只裁切好了梯形卡槽。

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

如果这是真， 他们率 就应该是一样。

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分量应该等於乘以所以同样 这里x分量。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只是两长度为 1 直角三角形之。

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，两分别长 a 和 b，长 c。

Arrange them so that their hypotenuses form a tilted square.

将它们排列起来，使其形成一个倾正方形。

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

直角三角形是多少 直角三角形是多少。

And you could do your SOH-CAH-TOA.

你们知道 cos是邻除以。

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了。

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

好吧，它正沿着，沿着一个倾角度慢慢前行。

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.

他们都为着名勾股定理提出了简洁证明，该定理指出， 对于一个直角三角形，一条直角平方加上另一条直角平方等于平方。

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，没有任何迹象表明有上升轴线。

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， 古代历史学家描述就是，他们实际上试图画一个直角三角形， 两个入口分别位于两端。

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，其中球面矩形高度是，其投影是其中一个直角。

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平方是81， 再加上81，因此长度就是162平方根， 大约是12.7。