Compare triangle sides with squared values. Identify angle behavior fast. Review exact relations, area, perimeter, exports, graph, and practical interpretation.
Enter three sides. The tool sorts them, tests triangle validity, compares squared values, and reports whether the largest angle is acute, right, or obtuse.
| Triangle | Sides | Largest Side | z² | x² + y² | Result |
|---|---|---|---|---|---|
| Example 1 | 3, 4, 5 | 5 | 25 | 25 | Right |
| Example 2 | 5, 6, 7 | 7 | 49 | 61 | Acute |
| Example 3 | 3, 4, 6 | 6 | 36 | 25 | Obtuse |
| Example 4 | 8, 15, 17 | 17 | 289 | 289 | Right |
The calculator first sorts the sides. Let x and y be smaller. Let z be largest.
Right triangle: z² = x² + y²
Acute triangle: z² < x² + y²
Obtuse triangle: z² > x² + y²
This is the Pythagorean inequality idea. It extends the classic theorem. The comparison reveals the largest angle type without measuring angles directly.
For extra outputs, the calculator uses Heron’s formula for area:
s = (x + y + z) / 2
Area = √[s(s-x)(s-y)(s-z)]
It also computes altitude to the largest side:
Altitude = 2 × Area / z
Always enter positive lengths. The calculator rejects impossible triangles. It automatically sorts sides, so entry order does not affect the final classification.
The Pythagorean inequality theorems help classify triangles using only side lengths. This is useful in geometry, drafting, surveying, design checks, and classroom practice. You do not need angle measures first. The side comparison alone reveals the angle nature.
Start by ordering the sides from shortest to longest. Compare the square of the largest side with the sum of the squares of the other two sides. If both values match, the triangle is right. If the largest square is smaller, the triangle is acute. If it is larger, the triangle is obtuse.
This calculator performs the comparison instantly. It also checks triangle validity. That step matters because some side sets cannot form triangles at all. After validation, the tool reports the relation, explains the theorem result, and adds useful measures such as perimeter, area, and altitude to the longest side.
Students can verify homework and practice pattern recognition. Teachers can show how side lengths control angle behavior. Builders and engineers can make quick side-based geometry checks. Data export helps with record keeping and worksheets. The graph also makes the comparison easier to understand.
Use consistent units for all three sides. Review the ordered sides before interpreting the result. A tiny difference can happen with decimal entries, so careful precision settings help. When you want a clean report, download the result and keep the theorem summary with the measured values.
It classifies a valid triangle as acute, right, or obtuse by comparing the largest squared side with the sum of the other two squared sides.
No. The calculator sorts the three sides automatically. It always compares the largest side against the other two smaller sides.
The calculator checks the triangle inequality first. If two smaller sides do not exceed the largest side, it returns an invalid triangle message.
A right triangle appears when the square of the largest side equals the sum of the squares of the other two sides.
Area gives added geometric context. It helps users connect side classification with another important triangle measure for design and study work.
Yes. Decimal side lengths are supported. The precision field lets you control how many decimal places appear in the output.
The graph compares z² and x²+y². Their relative height visually confirms whether the triangle is acute, right, or obtuse.
The CSV file stores the result rows. The PDF file creates a clean report summary with entered sides, theorem relation, and key measures.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.