A 80-80-20 Triangle

In the previous issue of At Right Angles, we studied a geometrical problem concerning the triangle with angles of 130 ◦ , 20 ◦ and 30 ◦ . We made the comment that the problem belongs to a class of geometrical problems dealing with triangles with numerous lines drawn within them, intersecting at angles whose measures are an integer number of degrees; we are required to find the measure of some indicated angle. In this note, we study another problem of this genre—a particularly famous such problem. We present a trigonometric solution as well as a ‘pure geometry’ solution.

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