Classifying Triangles

Date: 06/04/2002 at 20:50:30
From: George Springfiel
Subject: triangles

Tell whether the triangle is right, acute, or obtuse:

1. 4,5,6

2. 15,20,25

3. 5,7,10

Date: 06/04/2002 at 22:35:01
From: Doctor Ian
Subject: Re: triangles

Hi George,

In a right triangle, the square of the longest side is equal to 
the sum of the squares of the other two sides.  (This is the 
Pythagorean theorem.)

Imagine a right triangle, 

   |\
   | \ c           a^2 + b^2 = c^2
 a |  \
   |___\
     b

Now imagine that we make the triangle acute, by keeping a and b 
the same length, but making c a little shorter.  How could you 
detect that just by looking at the squares of a, b, and c?

Now imagine that we make the right triangle obtuse, by making c a 
little longer, while keeping a and b the same length.  How could 
you detect that just by looking at the squares of a, b, and c? 

Can you take it from here?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/