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Isosceles Triangle Height Calculator — result sheet
Find the height, area, perimeter, and base angles of an isosceles triangle from its equal side and base.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: h = √(s²-(b/2)²); area = bh/2; perimeter = 2s+b; base angle = acos((b/2)/s).
Dropping the altitude from the apex bisects the base and creates two congruent right triangles. That right-triangle relationship supplies the height and the equal base angles.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Equal side length — units; minimum 1.0E-6; maximum 1000000000
- Base length — units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Equal side length | 5 |
| Base length | 6 |
Height: 4 units; area: 12 square units; each base angle: 53.13°.
Assumptions and limits
- The two equal sides are longer than half the base, so the triangle is non-degenerate.
- The triangle is Euclidean and all lengths use the same unit.
- The base angle is the interior angle between the base and either equal side.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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