Free · Triangle calculators 🔺

Right-Triangle Angles from Legs, Hypotenuse or Area

Calculate right-triangle angles from legs, hypotenuse or area with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • 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

Worked inputs Leg (a) = 3, Leg (b) = 4 give Hypotenuse (c) = 5, Area = 6, Angle α = 36.869898, Angle β = 53.130102. Values use the initial displayed units.

c² = a²+b²; A = ab/2; tan α = a/b; α+β = 90°

Worked example

Enter these known values and leave the other values blank.

Leg (a)
3 cm
Leg (b)
4 cm
Hypotenuse (c)
5 cm
Area
6 cm²
Angle α
36.8699 deg
Angle β
53.1301 deg

Assumptions and limitations

  • The legs a and b meet at 90°. Angle α faces leg a and β faces leg b. Both inferred acute angles use their positive principal branch.
  • Lengths and areas are converted before calculation. Clear an unknown measurement instead of supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π. Display rounding and measurement uncertainty are separate from the underlying arithmetic.

Common questions

Which measurements and inverse branch does this model use?

The legs a and b meet at 90°. Angle α faces leg a and β faces leg b. Both inferred acute angles use their positive principal branch.

Which angle faces leg a?

Angle α is opposite leg a, so tan α = a/b. The other nonright angle is β = 90°−α.

References

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

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