special triangles

Topic:
Triangles

There are two special right triangles

In the triangle below a represents the ratio of AC/BC, and b represents AB/BC.
Drag point A and notice what happens to the ratio as the triangle changes dynamically.

What does this mean for the ratio of these special right triangles? Side AC is opposite the 60 degree angle, while BC is the hypotenuse. Write the ratio using those terms.

Special triangle 2

a represents the ratio EC/BE.
Drag a vertice and notice what occurs in regard to the ratio?

What type of triangle is this? What does the ratio represent in terms of the sides? Think using the terminology from the previous triangle.