Triangle Tool
Find missing triangle sides and angles using five input methods. View area, perimeter, heights, medians, inradius, circumradius, triangle classifications, and an interactive diagram. Compare possible SSA solutions and export measurements or diagrams.
Table of Contents
Highlights
- Five solving methods: SSS, SAS, ASA/AAS, SSA and right triangles
- Interactive triangle diagram with draggable vertices
- Area, perimeter, angles, heights, medians and circle radii
- Handles both valid solutions in ambiguous SSA cases
- Adjustable precision, angle bars and CSV, JSON or image exports
How Triangle Tool Works?
A triangle has three sides (a, b, c) opposite angles (A, B, C). The angles sum to 180°. For three known sides (SSS), the law of cosines determines the angles. For two sides and their included angle (SAS), it first finds the opposite side. With two angles and side c (ASA/AAS), the third angle follows from the angle sum and the law of sines gives the remaining sides.
The SSA method may yield zero, one or two valid triangles because an inverse sine can correspond to two angles. The right-triangle mode accepts any two independent measurements including at least one side, using right-triangle trigonometry or the Pythagorean theorem. The diagram lets you drag vertices to explore a revised triangle.
From the solved side lengths, the tool computes the semi-perimeter s, area K by Heron’s formula, perimeter P, heights, radii and medians:
| Property | Formula |
|---|---|
| Perimeter | P = a + b + c |
| Height to side a | ha = 2K/a |
| Inradius | r = K/s |
| Circumradius | R = abc/(4K) |
| Median to side a | ma = ½√(2b² + 2c² − a²) |
Equivalent formulas apply to sides b and c. The results also identify the triangle by side equality (equilateral, isosceles or scalene) and angle type (acute, right-angled or obtuse), display angle bars, and provide CSV, JSON, SVG, PNG and copyable outputs.
Practical Use Cases
Students: Check geometry homework by entering three sides, two sides and an included angle, or two angles and a side, then compare calculated sides, angles and the 180° angle sum.
Builders and carpenters: Evaluate a triangular brace or roof section using measured sides, then review its perimeter, area, heights and angle classification.
Architects and designers: Explore alternate triangle proportions on the draggable diagram and inspect how dimensions, area and medians change.
Surveyors: Work with two sides and a non-included angle to check whether one or two geometrically possible layouts fit the measurements.
Engineers: Examine right-triangle leg and hypotenuse relationships and check radius, median or altitude values for a preliminary geometric sketch.
Accuracy and Limitations
Calculations use JavaScript double-precision floating-point arithmetic, with displayed values rounded to a selected 2, 3, 4, 5, 6 or 8 decimal places. Inputs must describe a non-degenerate triangle, and SSA inputs can produce two distinct valid solutions. Very large, very small or nearly collinear dimensions can lose numerical accuracy, particularly for area, radius and angle calculations. Right-triangle mode requires at least one side, and two acute angles alone do not fix the size. Dragging a vertex changes the solved geometry without rewriting the original form inputs.
