Free · Triangle calculators 🔺

Equal-Leg Right Triangle Hypotenuse and Altitude

Calculate equal-leg right triangle hypotenuse and altitude with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
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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 The two equal sides (B) = 3 give Hypotenuse (A) = 4.2426407, Height (H) = 2.1213203, Area = 4.5, Perimeter = 10.242641. Values use the initial displayed units.

c = a√2; altitude to c = c/2; A = a²/2; P = 2a+c

Worked example

Enter these known values and leave the other values blank.

The two equal sides (B)
3 cm
Hypotenuse (A)
4.243 cm
Height (H)
2.1213 cm
Area
4.5 cm²
Perimeter
10.243 cm

Assumptions and limitations

  • The equal legs meet at 90°. The height control is the perpendicular altitude to the hypotenuse, not either equal leg.
  • 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.
  • To recover a leg from area or perimeter, supply the altitude or hypotenuse too; the retained inverse rules use those known quantities together.

Common questions

Which measurements and inverse branch does this model use?

The equal legs meet at 90°. The height control is the perpendicular altitude to the hypotenuse, not either equal leg.

Which height does this equal-leg right triangle use?

It uses the perpendicular altitude to the hypotenuse. That altitude is half the hypotenuse; it is not one of the equal perpendicular legs.

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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