Morley Triangle Calculator
First/interior Morley equilateral triangle SIDE8Rsin(A/3) sin(B/3) sin(C/3), strictly valid sides, same units. Not externaltrisectorvariantsor full coordinates.
Description
The first interior Morley triangle is formed by adjacent interior angle trisectors of a nondegenerate triangle.
The first interior Morley triangle is formed by adjacent interior angle trisectors of a nondegenerate triangle.1
This tool calculates its equilateral side length from the original side lengths without returning intersection coordinates.
When to use Morley Triangle Calculator
This tool calculates its equilateral side length from the original side lengths without returning intersection coordinates.
How to use Morley Triangle Calculator and how it works
- Prepare side a, side b, side c, using the input definitions and matching units below.
- Enter the required fields and run Morley Triangle Calculator.
- Read result.value using the units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| sideA | Side A. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| sideB | Side B. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| sideC | Side C. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Require positive triangle side lengths satisfying all strict triangle inequalities. Compute Heron's area, circumradius abc/(4*area) and the three angles by the cosine rule. Return 8*R times the product of sine of each angle divided by three. Output is the first interior Morley triangle's side length in the original length unit, not area, coordinates or external-trisector variants.
morleySide=8*R*sin(A/3)*sin(B/3)*sin(C/3) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Geometric length in the supplied radius, side or curve-scale unit. | number |
{
"input": {
"sideA": 3,
"sideB": 4,
"sideC": 5
},
"output": {
"result": {
"value": 0.6475176883770992
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Incircle Radius Calculator for a complementary operation: A triangle's inradius equals its area divided by its semiperimeter.
Use Fermat Point Triangle Calculator for a complementary operation: The Fermat point minimizes total Euclidean distance to the vertices of a nondegenerate triangle.
References
-
Morley Triangle Calculator — tool.io
Similar or alternative tools
- Incircle Radius Calculator
A triangle's inradius equals its area divided by its semiperimeter.
- Fermat Point Triangle Calculator
The Fermat point minimizes total Euclidean distance to the vertices of a nondegenerate triangle.