Special Triangles: Going Beyond 30 – 60 – 90 and 45 – 45 – 90
Starting with the standard special triangles, the 30 – 60 – 90 and the 45 – 45 – 90, we discovered other special triangles. A special triangle is one that has angle values and side lengths that can be expressed exactly. Starting with our two standard special triangles, we applied half angle formulas to an angle from each triangle, which resulted in infinitely many different special triangles. Using the angles expressed in radians from our new special triangles, we derived other special triangles by applying addition and subtraction formulas. We also found that each third whole number angle between 3 degrees and 90 degrees is a part of a special triangle.