There is a set of triangles, in each of which the smallest angle does not exceed 36o . A new one is formed from these triangles according to the following rule: the smallest side of the new one is equal to the sum of the smallest sides of these triangles, its middle side is equal to the sum of the middle sides, and the largest is the sum of the largest ones. Prove that the sine of the smallest angle of the resulting triangle is less than 2sin18o . geometrytrigonometryanglesgeometric inequality