Triangle Calculation Formulas
SSS — Heron's Formula: s = (a+b+c)/2, Area = √(s(s-a)(s-b)(s-c))
SAS — Find Side: c² = a² + b² - 2ab·cos(C)
SAS — Area: Area = 0.5 × a × b × sin(C)
Base + Height: Area = 0.5 × base × height
Note: Angles are in degrees. The triangle inequality must be satisfied for valid results.
Triangle Calculator — Sides, Angles & Area
The 3-4-5 triangle is the most important tool in a builder’s mathematical toolkit — used daily for checking square. This calculator solves any triangle: sides, angles, area, perimeter, and height.
Key Formulas
| Formula | Equation | Use |
|---|---|---|
| Pythagorean | a² + b² = c² | Right triangles, checking square |
| Area | ½ × base × height | Simple area |
| Heron’s | √(s(s-a)(s-b)(s-c)) | Area from 3 sides |
| Law of Cosines | c²=a²+b²−2ab·cos(C) | Unknown side/angle |
Builder’s Right-Angle Triangles
| Ratio | Example | Use |
|---|---|---|
| 3:4:5 | 3m, 4m, 5m | Most common square check |
| 6:8:10 | 6m, 8m, 10m | Larger setouts |
| 5:12:13 | 5m, 12m, 13m | Long diagonal checks |
Frequently Asked Questions
How do builders check square?
3-4-5 method: measure 3m along one wall, 4m along the other, diagonal should be exactly 5m. Scale up as needed (6-8-10).
How to calculate triangle area?
½ × base × height. Or Heron’s formula from three sides: s=(a+b+c)/2, Area=√(s(s-a)(s-b)(s-c)).
What is the 3-4-5 rule?
Based on Pythagorean theorem (3²+4²=5²). If sides are 3, 4, 5, the angle between 3 and 4 is exactly 90°.
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