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• Are there any triangles where all three sides are whole numbers as well as all three angles in whole degrees. posted (4 months, 3 weeks) ago
  there any triangles where all three sides are whole numbers as well as all three angles in whole de…

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• Are there any triangles where all three sides are whole
  

  That is the problem with whole number problems. I have used things like if(int(f(x))-f(x)=0, this, else this) in spread sheets to check for whole numbers. Of course this only checks out to the precision of the computer. This problem is harder because I would also have to look for answers where the decimal part could be a fraction, because if they have a fractional part that whole triangle could be made bigger until all the sides are whole. There is probably a way around that.
  
  Anyhow, the list of these triangles is not that large. There are 90 of them.
  90-89-01
  90-87-02
  .
  90-01-89
  
  I guess I should search threw that set for triplets of sides that are rational numbers, not really sure how though. I am sleeping on this one.
  - written 4 months, 3 weeks ago

• Are there any triangles where all three sides are whole
  

  You showed that a lot of the equilateral triangles work. I had not even been thinking about them. That’s great. I was thinking about the right triangles and now I have to add the isosceles. Maybe I could power my way threw some fancy logic with a spread sheet for all 360 degrees.
  - written 4 months, 3 weeks ago

• Are there any triangles where all three sides are whole
  

  Cool. I have been trying to figure that one out. I don’t think there are any cases where all of them (both sides and angles) are whole numbers. I can’t really prove it though. Thanks
  - written 4 months, 3 weeks ago

• Are there any triangles where all three sides are whole
  

  You can figure out the angles of the 3-4-5 this way:
  1) the 5 has to be the hypotenuse because it is the largest one
  
  2) take the inverse tangent of 3/4 to get one of the angles that is not the 90.
  3) take the inverse tangent of 4/3 to get the other one.
  
  OR
  2) take the inverse cosine of 4/5 for one of the angles that is not the 90.
  3) take the inverse sine of 3/5 to get the other one.
  
  I learned that in SUNY Alfred University
  - written 4 months, 3 weeks ago

• Are there any triangles where all three sides are whole
  

  A 3-4-5 sided right triangle has angles 36.869897645844021296855612559093, 53.130102354155978703144387440907, and 90 degrees.
  
  A right triangle with angles 30-60-90 will have sides in the ratio 1:2:sqrt(3)
  
  Check it out.
  - written 4 months, 3 weeks ago

BobMcArthur's conversations are tagged:

math, Triangle, whole numbers