Triangle Solver

📖 Introduction

Solving a triangle is a core exercise in lower secondary geometry and upper secondary trigonometry. Given three sides, two sides with the included angle, two angles with the included side, or two angles with an opposite side, the remaining sides and angles are determined uniquely. This tool handles each of those four cases: with three sides it inverts the law of cosines to recover the three angles; with two sides and the included angle it first finds the third side by the law of cosines and then the remaining angles by the law of sines; with two angles it completes the angle sum and then applies the law of sines. Once solved it also reports the area via Heron formula, the perimeter, the height on a chosen side, the circumradius and the inradius, and it classifies the triangle as right, acute or obtuse. A proportionally scaled diagram is drawn beside the results with sides and angles labelled, so you can sanity check the answer at a glance. Angles may be entered and read in degrees or radians, and impossible combinations are rejected with a clear message rather than a wrong answer. A scaled diagram sits beside every result, drawn from the solved side lengths so that the shape on screen visually matches the numbers in the table; a badly wrong input usually shows up immediately as an impossible looking triangle. The tool also reports whether the triangle is right angled, acute or obtuse, which is a common exam question in its own right. Switching between degrees and radians lets the same page serve both school geometry, where degrees are standard, and later trigonometry or physics work where radians are expected. Input validation catches the triangle inequality before any calculation is attempted, so impossible side combinations produce a clear message instead of a page of NaN values.

✨ Features

• Four given-case modes: three sides, two sides plus included angle, two angles plus included side, two angles plus an opposite side.
• Solves every side and angle automatically and tells you whether the law of sines or cosines was used.
• Reports area, perimeter, height on a given side, circumradius and inradius together.
• Classifies the triangle as right angled, acute or obtuse on its own.
• Draws a scaled diagram with the sides and angles labelled directly on it.
• Accepts and outputs angles in either degrees or radians.

🚀 How to use

1. Pick the type of data you already have from the given-case list.
2. Enter the corresponding side lengths or angles.
3. Choose whether angles are measured in degrees or radians.
4. Press solve and the full result plus the diagram appear on the right.
5. Press a preset to load a classic triangle such as 3-4-5 or 5-12-13.

⚠️ Notes

• Triangle inequality. Any two sides must add up to more than the third, otherwise the tool reports that no triangle exists.
• Angle unit. Switching between degrees and radians reinterprets values already typed in, so check the unit first.
• Floating point. Inverse trigonometric results carry a tiny rounding error and are shown to four decimals.
• Diagram scale. The drawing is fitted to the canvas and its aspect ratio is adapted, so it is not to physical scale.
• Degenerate cases. An included angle of 0 or 180 degrees has no solution and is refused.