KEVOS® MAKEOS · Geometry
Triangle Solver
What are the missing sides, angles and area of this triangle?
Solve any triangle from three sides, two sides and the included angle, or two angles and the included side, using the laws of sines and cosines.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known values | choice | Choose the combination you know. |
| Side a | mm | Side opposite angle A. |
| Side b | mm | Side opposite angle B. |
| Side c | mm | Side opposite angle C. |
| Angle A (opposite a) | ° | Interior angle opposite side a (used with two angles and the included side). |
| Angle B (opposite b) | ° | Interior angle opposite side b (used with two angles and the included side). |
| Angle C (opposite c) | ° | Interior angle opposite side c (used with two sides and the included angle). |
Method and formulas
- Three sides: A = arccos((b² + c² − a²) ÷ 2bc), and similarly for B; C = 180° − A − B.
- Two sides and angle C: c = √(a² + b² − 2ab cos C), then the remaining angles by the law of cosines.
- Two angles and side c: C = 180° − A − B; a = c sin A ÷ sin C; b = c sin B ÷ sin C.
- Area = ½ab sin C; circumradius R = a ÷ (2 sin A); inradius r = area ÷ semi-perimeter.
- Example: sides 30, 40 and 50 mm give angles of 36.87°, 53.13° and 90° and an area of 600 mm².
Limitations
- Two sides with a non-included angle (the ambiguous case) is not offered; convert it to one of the listed cases.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find hole positions and distances on brackets and frames
- Check angles of gussets and braces
- Solve layout problems without CAD
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- All three sides
- All three angles
- Area
- Perimeter
- Circumscribed and inscribed circle radii
Interpreting the result
- Use the inradius and circumradius to check fit of round features in triangular spaces.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 95–102. Topic reference; no source tables or recommended settings are reproduced.
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