Algorithm for triangles classification

Introduction

Triangles are classified depending on relative sizes of their elements.

As regard their sides, triangles may be:

• Scalene (all sides are different)
• Isosceles (two sides are equal)
• Equilateral (all three sides are equal)

And as regard their angles, triangles may be:

• Acute (all angles are acute)
• Right (one angle is right)
• Obtuse (one angle is obtuse)

In this tip we will develop an algorithm that determines the type of a triangle, given its sides.

Using the code

The algorithm below was implemented in the Lua language using the ZeroBrane Studio IDE:

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local function triangleType(a,b,c)
  local bySide,byAngle = nil

  if (a < (b + c) and b < (a + c) and c < (a + b)) then

    --Type of the triangle by sides
    if ( a == b and b == c ) then
      bySide = 1 -- Equilateral
    elseif (a == b or b == c or a == c) then
      bySide = 2 -- Isosceles
    else
      bySide = 3 -- Scalene
    end  

    --Type of the triangle by Angle
    if (a^2 == b^2 + c^2) or (b^2 == a^2 + c^2) or (c^2 == a^2 + b^2)  then
      byAngle = 1 -- Right
    elseif (a^2 > b^2 + c^2) or (b^2 > a^2 + c^2) or (c^2 > a^2 + b^2)  then
      byAngle = 2 -- Obtuse
    else
      byAngle = 3 -- Acute
    end

  end

  return bySide,byAngle

end  
local bySideTypes = {"Equilateral","Isosceles","Scalene"}
local byAngleTypes = {"Right","Obtuse","Acute"}

print("Triangle Type\n")
print("Enter the value of A side: ")
local a = tonumber(io.read())
print("Enter the value of B side: ")
local b = tonumber(io.read())
print("Enter the value of C side: ")
local c = tonumber(io.read())

local bySide,byAngle = triangleType(a,b,c)

if (bySide ~= nil) then
  print ("The type of the triangle is " .. bySideTypes[bySide] .. " and " .. byAngleTypes[byAngle])
else
  print ("These sides do not form a triangle")
end

Points of Interest

The following points should be taken into account for the understanding of the algorithm:

1. The sum of the lengths of any two sides of a triangle is greater than the length of the third side
2. To obtain the type of the triangle according to its angles, we use the Pythagorean theorem
3. In the Lua language, a function can return more than one value.
4. For the sake of “good practices”, we have resolved to encode the types of triangles in an array

References

1. https://study.com/academy/lesson/types-of-triangles-their-properties.html
2. https://www.youtube.com/watch?v=I2Lt-jU3IJc

Conclusion

The source code for this algorithm is available on GitHub at:  MathAlgorithms

That’s all, folks!