A line through a vertex of a triangle cuts it in two similar triangles with √3 as the ratio between correspondent sides.
Find the angles of the given triangle.
If you start with a 306090 triangle,
draw a line from the right angle perpendicular to the hypotenuse.
This divides the original triangle into 2 306090 triangles with the ratio of corresponding sides being √3.
I do not know if this is the only solution.

Posted by Larry
on 20230820 11:51:35 