Rapports Trigonométriques Clés1 : 1 : √2 & 1 : √3 : 2
Solveur de Triangles Rectangles Particuliers (45-45-90 & 30-60-90)
Solve isosceles 45°-45°-90° and half-equilateral 30°-60°-90° triangles from a single side length with exact rationalized radical denominators. For arbitrary right triangles with two custom sides, return to our Pythagoras equation solver.
Rationalized DenominatorsAngle & Radical SVG OverlayShortcut vs. Pythagorean Check
Result updated: 45-45-90 triangle legs are 5 and 5, hypotenuse is 5radical 2.
Special Right Triangles Calculator
Select triangle type and enter any one side to rationalize denominators cleanly.
Known Side Given
Enter a strictly positive side length for the selected special right triangle.
Preset Examples
Ratio 1 : 1 : √2Angles: 45° / 45° / 90°
Leg a (45°)
5
≈ 5
Leg b (45°)
5
≈ 5
Hypotenuse c (90°)
5√2
≈ 7.0711
Area = 12.5Perimeter = 17.0711
Shortcut Ratio (1 : 1 : √2) vs. Full Pythagorean Verification
1. Geometric Shortcut (45-45-90)
- 1. Apply the 45°-45°-90° ratio (1 : 1 : √2): both legs are equal (a = b = 5).
- 2. Multiply leg by √2 to find the hypotenuse: c = a√2 = 5√2.
- 3. Pythagorean check: √(5² + 5²) = √50 ≈ 7.0711.
2. Standard Pythagorean Theorem Check (a² + b² = c²)
a² = (5)² = 25
b² = (5)² = 25
a² + b² = 50
√(a² + b²) = 7.0711 = c (5√2)
Fiche Mémo des Rapports des Triangles Particuliers
| Triangle Angles | Side Ratio | Leg Formula | Hypotenuse Formula |
|---|---|---|---|
| 45° - 45° - 90° | 1 : 1 : √2 | a = b = (c√2) / 2 | c = a√2 |
| 30° - 60° - 90° | 1 : √3 : 2 | a = c/2, b = a√3 = (b√3)·(1) | c = 2a = (2b√3)/3 |