Prove that the hypotenuse is larger than the leg in a right-angled triangle.

Let AB be the hypotenuse of a right-angled triangle, and BC – the leg of this triangle and, accordingly, angle B, this is the angle between them. It is known that in a right-angled triangle the ratio of the hypotenuse to the leg is equal to the cosine of the angle between them: BC / AB = cos (B) Hence the leg is equal to the hypotenuse multiply by the angle B. BC = AB * cos (B) (1) It is known that the cosine of an angle can have values ​​from “-1” to “1”. cos (B) will be “1” if the angle B is “0”, but there cannot be such an angle in a triangle. It turns out that the angle В ≠ 0, and hence cos (В) <1. From expression (1) it can be seen that the leg is less than the hypotenuse, since equals the hypotenuse times a number less than “1”. BC <AB.