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Isosceles Triangle Altitudes to Base and Equal Leg

Calculate isosceles triangle altitudes to base and equal leg 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) = 5, Base (b) = 6 give Height to apex (hb) = 4, Height from leg (ha) = 4.8. Values use the initial displayed units.

hbase² = a²−(b/2)²; hleg = b hbase/a

Worked example

Enter these known values and leave the other values blank.

Leg (a)
5 cm
Base (b)
6 cm
Altitude to base
4 cm
Altitude to equal leg
4.8 cm

Assumptions and limitations

  • The altitude to the base and the altitude to an equal leg generally differ. The shared enclosed area is computed internally to relate both altitudes.
  • 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 altitude to the base and the altitude to an equal leg generally differ. The shared enclosed area is computed internally to relate both altitudes.

Why are there two altitudes in an isosceles triangle?

An altitude depends on the side chosen as the base. The two values satisfy b hbase = a hleg because both products are twice the same enclosed area.

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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