Whole Number Interior and Lengths Triangle - Does It Exist?

[Ted_Grendy]

Hi all

I was wondering if someone could help with a strange Triangle problem.

I am trying to determine whether or not there exists a triangle (right angle or otherwise) where the interior angles and the length of the sides are all whole numbers.

Does anyone have any ideas?

Thanks

 

[Harry_the_cat]

Hi all

I was wondering if someone could help with a strange Triangle problem.

I am trying to determine whether or not there exists a triangle (right angle or otherwise) where the interior angles and the length of the sides are all whole numbers.

Does anyone have any ideas?

Thanks

An equilateral triangle with an integer side length would work.

 

[Deleted member 4993]

Hi all

I was wondering if someone could help with a strange Triangle problem.

I am trying to determine whether or not there exists a triangle (right angle or otherwise) where the interior angles and the length of the sides are all whole numbers.

Does anyone have any ideas?

Thanks

Angles measured in what units (radian?, degrees?)

Sides measured in what units (inches?, mm?)

 

[Ted_Grendy]

Angles measured in what units (radian?, degrees?)

Sides measured in what units (inches?, mm?)

Angles measured in Degrees and sides measured in mm.

 

[Harmless Drudge]

Hi all

I was wondering if someone could help with a strange Triangle problem.

I am trying to determine whether or not there exists a triangle (right angle or otherwise) where the interior angles and the length of the sides are all whole numbers.

Does anyone have any ideas?

Thanks

You want all of the angles to be whole number angles and the sides to be whole number sides? One if the most fruitful exercises when asked to find commonality can be to see whether regularity (the most extreme commonality of features) is up to ththe task.

For example, if the question asked for a quadrilateral, instead of a triangle, would a regular quadrilateral work? What is a quadrilateral with 4 of the same angle and 4 of the same side? Is there a triangle formed by the same premise?

You can then explore other triangles using trigonometry and algebra (think Law of Cosines), but it may be beyond the reach they expect you to have to answer the question. It seems more a conceptual question than a strict and elegant one.

 

[jtayag0622]

Hi all

I was wondering if someone could help with a strange Triangle problem.

I am trying to determine whether or not there exists a triangle (right angle or otherwise) where the interior angles and the length of the sides are all whole numbers.

Does anyone have any ideas?

Thanks

equilateral triangles. As we all know, one of the corollaries of the Isosceles Triangle Theorem is "an equilateral triangle is also equiangular." This means that "an equilateral triangle has three 60° angles" (which is also a corollary of the Isosceles Triangle Theorem). Just draw a 60° angle, make its sides equal and wholes, then draw the third side. You should have all the sides and angles equal and whole.