Free · Triangle calculators 🔺

Right-Triangle Side Ratios, Angles and Area

Calculate right-triangle side ratios, angles and area with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
  • Private in your browser
  • No signup
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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 Side length a = 3, Side length b = 4 give Side length c = 5, Area = 6, Angle α = 36.869898, Angle β = 53.130102. Values use the initial displayed units.

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

Worked example

Enter these known values and leave the other values blank.

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
Area
6 cm²

Assumptions and limitations

  • Two perpendicular legs define the right triangle. The angle opposite a is α; the complementary angle is β. A side and an acute angle can recover the other dimensions.
  • 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?

Two perpendicular legs define the right triangle. The angle opposite a is α; the complementary angle is β. A side and an acute angle can recover the other dimensions.

How does triangle area connect the two legs?

For perpendicular legs a and b, area is ab/2. A known area and one positive leg recover the other leg by dividing twice the area by the known leg.

References

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

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