This triangle solver finds the missing sides and angles of any triangle from the parts you know — three sides, two sides and an angle, or two angles and a side. It is the go-to for setting out braces, roof slopes, rafters, ramps, and any layout where two measurements must fix a third.
Which rule applies
The method depends on what you know. With all three sides (SSS) or two sides and the included angle (SAS), the cosine rule unlocks the rest. With two angles and a side (ASA or AAS), the angles sum to 180° and the sine rule finds the sides. For right-angled triangles, Pythagoras and basic trigonometry suffice. The solver picks the right approach automatically and returns every side and angle.
This matters in the shop and on site because triangles are how you transfer angles and check square. The 3-4-5 method for squaring a corner is just a right triangle; a diagonal brace, a hip rafter, and a staircase stringer are all triangle problems in disguise.
From triangle to workpiece
Once the solver gives the angles, those become your saw and bevel settings; the sides become your cut lengths. Knowing, say, the length of a brace and the angles at each end means you can cut it to fit first time rather than scribing in place. Always sanity-check that the inputs can form a valid triangle — the longest side must be shorter than the sum of the other two.
A right-angled brace rises 600 mm over a 800 mm run; how long is the brace?
- It's a right triangle, so use Pythagoras.
- Brace² = 600² + 800² = 360000 + 640000 = 1,000,000.
- Brace = √1,000,000 = 1000 mm.
The diagonal brace is exactly 1000 mm — a classic 3-4-5 (600-800-1000) right triangle.
