special triangles


There are two special right triangles

In this special right triangle, B is 60, and C = 30. The ratio of AC/BC is represented by a, and the ratio AB/BC is represented by b.
Drag point A and notice what happens to the ratios as the triangle changes dynamically.

What does this mean for the ratio of these special right triangles? Side AB is opposite the 30 degree angle, while BC is the hypotenuse. Write the ratio using those terms.

Special triangle 2

In this special right triangle B is 45 and E is 45. The ratio EC/BE is represented by a.
Drag a vertice and notice what occurs in regard to the ratio?

This triangle would be classified as what type of triangle? Think in terms of angles and sides. What does the ratio represent in terms of the sides? Think using the terminology from the previous triangle.