Free · Mathematics models
Triangle Heights in Four Forms
Relate heights, areas, side lengths and angles in general, equilateral, isosceles and right triangles.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- 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
A 3–4–5 triangle has area 6 square units and heights 4, 3 and 2.4 to its respective sides.
Each height=2×area/base; general area follows Heron’s formula.
Worked example
Enter these known values and leave the other values blank.
- a
- 3 cm
- b
- 4 cm
- c
- 5 cm
- hᵃ
- 4 cm
- hᵇ
- 3 cm
- hᶜ
- 2.4 cm
- α
- 36.87 deg
- β
- 53.13 deg
- γ
- 90 deg
- Area
- 6 cm²
- Perimeter
- 12 cm
Assumptions and limitations
- Side lengths are positive. A nondegenerate general triangle has each pair of sides summing to more than the third. All four captured triangle forms remain available.
- Heights to oblique bases may meet extended side lines. Side-only areas and principal angle inverses do not encode mirrored orientation.
- Measurement uncertainty and spherical triangles are omitted.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
Side lengths are positive. A nondegenerate general triangle has each pair of sides summing to more than the third. All four captured triangle forms remain available.
What does this model leave out?
Measurement uncertainty and spherical triangles are omitted.
References
Model requirements: Every pair of sides must exceed the third side. Authored accessible explanations preserve each captured diagram mode and its geometric relationships.