>>11906305If you proportionally enlarge every side of a triangle, the resulting triangle is called similar. That is, if you take any side of the original triangle and the same side of the old triangle, and divide one by the other, you will get the same result if you take any other side - the enlargement factor. Any two similar triangles have the exact same angles of the corners, because enlarging the sides does not affect the angles.
Trigonometry makes two observations. First, that to describe any right angled triangle, it is enough to specify only a side length and an angle of the triangle, or alternatively, it is enough to specifiy just two side lengths. Second, every right angled triangle where a certain angle is given is similar to any other right angled triangle with that certain angle.
The observations leads to the following conclusion: given a right angled triangle with some angle , then the ratio of any two sides is equal to the ratio of the same two sides of any other right angled triangle with the same angle. So if you fix a side and the angle, any ratio between the sides is a constant for the right angled triangled of that angle, which we call etc. Alternatively, if you are given two side lengths, you can calculate the third using Pythagoras' theorem, and use that to calculate all the trigonometric functions of the angle of the triangle. It turns out that in the cases of triangles, there is a 1:1 correspondence with possible angles and values of or other trig functions - so once you know the sine of an angle, you can find out what the actual angle is.
