Isosceles Triangle Altitude Calculator
Compute the altitude of an isosceles triangle with precision. Handles degenerate cases and provides formulas for students and professionals.
About
An isosceles triangle has at least two sides of equal length. The altitude drawn from the vertex connecting the two equal sides to the base bisects the base perpendicularly. This symmetry simplifies calculations significantly compared to scalene triangles.
This calculator determines the height (h) when the congruent side length (a) and the base width (b) are known. It automatically checks for the "Triangle Inequality Theorem" to ensure the inputs form a valid geometric shape.
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Formulas
Using the Pythagorean theorem on the bisected right triangle:
h = √a2 − b24
Condition for validity: 2a > b.
Reference Data
| Parameter | Symbol | Relation to Altitude |
|---|---|---|
| Equal Side | a | Hypotenuse of the internal right triangle |
| Base | b | b2 is the leg of the internal right triangle |
| Apex Angle | θ | h = a cos(θ/2) |
| Base Angle | β | h = b2 tan(β) |
Frequently Asked Questions
The triangle is impossible (degenerate). The tool will output a calculation error or imaginary number indicator because a triangle cannot close if one side is longer than the sum of the others.
Only in an isosceles triangle (for the altitude drawn to the unequal base) and in an equilateral triangle. In scalene triangles, the altitude does not split the base into equal parts.
Once you have the altitude h, the area is simply b × h2.