Free · Geometry and function relationships

Right Triangle Sides and Acute Angles

Choose two sides, one side and an acute angle, or area and a side. The legs are perpendicular and the two acute angles add to 90°.

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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, c1 = 5, angle_alfa1 = 36.86989764584402129685561255909341065759157140070955794402796738.

c²=a²+b²; tan(α)=a/b; A=ab/2

Worked example

Enter these known values and leave the other values blank.

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

Assumptions and limitations

  • Choose two sides, one side and an acute angle, or area and a side. The legs are perpendicular and the two acute angles add to 90°.
  • 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?

Choose two sides, one side and an acute angle, or area and a side. The legs are perpendicular and the two acute angles add to 90°.

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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