sin of smallest angle less tahn 2 \sin 18^o, constructing triangle from triangle
Source: VII Soros Olympiad 2000-01 Round 1 , 10.8
July 4, 2021
geometrytrigonometryanglesgeometric inequality
Problem Statement
There is a set of triangles, in each of which the smallest angle does not exceed . 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 .