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Right-Triangle Missing Side with Acute-Angle Controls

Calculate right-triangle missing side with acute-angle controls 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 a = 3, b = 4 give c = 5, Angle α = 36.869898, Angle β = 53.130102. Values use the initial displayed units.

c² = a²+b²; a = c sin α; b = c sin β; 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
Angle α
36.87 deg
Angle β
53.13 deg

Assumptions and limitations

  • The positive hypotenuse is longer than either leg. Both nonright angles lie strictly between 0° and 90°. Angle α faces leg a.
  • 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 positive hypotenuse is longer than either leg. Both nonright angles lie strictly between 0° and 90°. Angle α faces leg a.

Can I enter an obtuse angle for a right triangle?

No. The two angles other than the right angle must each be positive and strictly below 90°.

References

Require acute right-triangle angles, a real positive hypotenuse and consistent three-side geometry.

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