Free · Arithmetic calculators ➗

Triangle Angle Weights & Relative Side Ratios

Convert three positive angle weights into triangle angles and obtain relative side lengths through the sine rule.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Equal angle weights give three 60° angles and side ratio 1:1:1.

α:β:γ = x:y:z, α+β+γ = 180°; opposite sides have ratio sin α : sin β : sin γ.

Worked example

Enter these known values and leave the other values blank.

Angle weight x
1
Angle weight y
1
Angle weight z
1
Angle α
60 deg
Angle β
60 deg
Angle γ
60 deg

Assumptions and limitations

  • x, y and z are angle weights, not side lengths. They are normalized to a total angle of 180°.
  • All weights and interior angles are positive. Angles are strictly below 180°.
  • The side-ratio note normalizes the side opposite α to one. No absolute side length or area is determined without an additional scale.
  • Arithmetic uses 64 significant decimal digits, with separate rounding for displayed values.

Common questions

Does angle ratio 1:1:2 mean side ratio 1:1:2?

The angles are 45°, 45° and 90°. The sine rule gives side ratio 1:1:√2 instead.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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