Free · Triangle calculators 🔺

Equal-Leg Triangle Base and Apex Angles

No. Enter the full base b. Its half b/2 appears only inside the formulas because the altitude bisects the base.

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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: Equal leg a 4, Full base b 4 gives Apex angle β 60, Equal base angle α 60.

cos α = b/(2a); β = π−2α

Worked example

Enter these known values and leave the other values blank.

Equal leg a
4 cm
Full base b
4 cm
Apex angle β
60 deg
Equal base angle α
60 deg

Assumptions and limitations

  • a is either equal leg and b is the entire base. Both are positive and b is strictly less than 2a. The two equal base angles α lie between 0° and 90°; the apex angle β lies between 0° and 180°. The captured altitude helper stays hidden. Angles alone give shape but no length scale.
  • 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.

Common questions

Is the entered base half the bottom side?

No. Enter the full base b. Its half b/2 appears only inside the formulas because the altitude bisects the base.

How many measurements are needed?

Use the worked example or a verified independent input pair or triple. Supplying dependent measurements does not add enough information; a consistent shape still needs a length scale.

Which input pairs support the retained inverse controls?

Use equal leg and full base; either length with the base angle; or either length with the apex angle. Two angle inputs alone give shape but no scale.

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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