The Problem of Acute, Obtuse, and Right Triangles


So our game has it that certain triangles rank above other triangles.
Let's start by getting some definitions:

*Acute Triangle= every angle is less that 90 degrees
*Obtuse Triangle = One angle is greater than 90 degree
*Right Triangle = One angle is exactly 90 degrees

You are likely familiar with the pythagorean theorem, which states that if you have a right triangle,

A^2 + B^2 = C^2
We can say the same for Acute and Obtuse triangles as well
For an Acute:
A^2 + B^2 >C^2
and For an Obtuse:
A^2 + B^2 < C^2

We want to think about what we are doing in terms of knowing C and B and looking for values of A:
A<=>(C^2-B^2)^.5

Our key is to find this value and determine where it falls within our range of A values given B and C.
We can then divide up our possible A values into three groups: the acutes, obtuses, and rights.
However, this is not as easy as it sounds when you think about it because (C^2-B^2)^.5 is usually not a rational number.
Also, for every C there are certain values of B that will only result in obtuse triangles.
I have an applet to help explain this as well as a graph.

Check out my BIG BAD UGLY ANSWER

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