Solve a triangle, then mark it out
Braces, gussets, cross members and squaring checks all come down to a triangle. Give this tool three sides, or two sides and the angle between them, and it returns every side, every angle, the area, and a set of vertex coordinates you can scribe straight onto the plate.
The math
From three sides the angles come from the law of cosines: angle A = arccos((b squared + c squared – a squared) / (2bc)), and likewise for B and C. From two sides and the included angle, the third side is a = square root of (b squared + c squared – 2bc cos A), then the remaining angles follow the same way. Area uses Herons formula, square root of s(s-a)(s-b)(s-c) where s is half the perimeter.
Laying it out
The coordinates place vertex A at the origin and vertex B along the X axis at distance c, with C found from the two sides meeting at A. Mark A and B on a baseline, then measure to C from both ends — the classic trammel method — and you have the triangle without a protractor.
Squaring with 3-4-5
The most useful triangle on a shop floor is 3-4-5: any triangle with sides in that ratio has a perfect 90 degree corner. Enter 3, 4, 5 and the tool confirms a right angle opposite the longest side — handy for squaring frames and layouts.
Related layout tools
For points around a circle, see the bolt circle calculator; to convert any radius and angle into coordinates, the polar coordinate calculator.
FAQ
What if the sides cannot form a triangle?
If any side is longer than the other two combined the triangle is impossible, and the tool flags it. Check your measurements — a brace that fails this test will not close.
Which angle is the included angle?
In the two-side mode, angle A sits between the two sides you enter, b and c. The side opposite it, a, is the one the tool solves for.