Free · Geometry and function relationships

Trigonometric Values and Right Triangle Sides

Evaluate the six trigonometric ratios for a signed angle, or calculate right-triangle measurements. Reciprocal ratios are undefined where their denominator is zero; inverse angles use principal branches.

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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.

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

Formula and method

For given = 0, a1 = 3, b1 = 4, angle = 30, c1 = 5, sin_print = 0.5, cos_print = 0.8660254037844386467637231707529361834714026269051903140279034895.

sin(θ)=opposite/hypotenuse; tan(θ)=opposite/adjacent

Worked example

Enter these known values and leave the other values blank.

Given...
0
Side length a
3 cm
Side length b
4 cm
Angle
30 deg
Side length c
5 cm
Angle α
36.87 deg
Angle β
53.13 deg

Assumptions and limitations

  • Evaluate the six trigonometric ratios for a signed angle, or calculate right-triangle measurements. Reciprocal ratios are undefined where their denominator is zero; inverse angles use principal branches.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

Evaluate the six trigonometric ratios for a signed angle, or calculate right-triangle measurements. Reciprocal ratios are undefined where their denominator is zero; inverse angles use principal branches.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

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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