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Triangle Angles, Heron Area and Boundary from Three Sides

No. This SSS workflow accepts three side lengths and keeps area, perimeter and all three angles as read-only outputs. Other triangle workflows provide different supported inverses.

  • Formula & worked example
  • Private in your browser
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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

Example in initial displayed units: a 3, b 4, c 5 gives α 36.8699, β 53.1301, γ 90, Area 6, Perimeter 12.

A = √(s(s−a)(s−b)(s−c)); s = (a+b+c)/2

Worked example

Enter these known values and leave the other values blank.

a
3 cm
b
4 cm
c
5 cm
α
36.87 deg
β
53.13 deg
γ
90 deg
Area
6 cm²
Perimeter
12 cm

Assumptions and limitations

  • Three positive sides must satisfy all strict triangle inequalities. Angles α, β and γ are opposite a, b and c respectively. All five remaining fields are one-way read-only results: three angles, area and perimeter. Degenerate and zero-sided triangles are excluded.
  • Clear unknowns before solving backward and select compatible units. Original reference drawings do not scale to entered values. Independently rounded boundary measurements can be incompatible at finite precision.
  • The Earth-radius selector uses the fixed source comparison 6,371,000 m, and the Sun-radius selector uses 695,700,000 m. These are reference conventions, not measurements of a particular body location. Soccer-field area uses a fixed 7,140 m² comparison.

Common questions

Can I enter the area to solve a missing side here?

No. This SSS workflow accepts three side lengths and keeps area, perimeter and all three angles as read-only outputs. Other triangle workflows provide different supported inverses.

How many measurements are needed?

Enter all three positive sides. Each side must be shorter than the sum of the other two.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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