KEVOS® MAKEOS · Geometry
Triangle from Two Sides and an Opposite Angle
Which triangles have these two sides and the angle opposite one of them?
Solve the ambiguous case of a triangle (two sides and an angle opposite one of them), giving none, one or two possible triangles with all sides, angles and areas.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Side a (opposite the known angle) | mm | Side opposite the known angle. |
| Side b | mm | The other known side. |
| Angle A (opposite side a) | ° | Known angle, opposite side a. |
Method and formulas
- sin B = b sin A ÷ a (law of sines).
- If sin B > 1 there is no triangle; if A is acute and a < b, B and 180° − B may both work.
- C = 180° − A − B; c = a sin C ÷ sin A; area = ½ ab sin C.
- Example: a = 40, b = 50, A = 40° gives 2 triangle(s).
Limitations
- Plane triangles only.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Solve layout problems where only two sides and one angle are known
- Check whether a linkage can assemble
- Find both positions of a mechanism
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Number of solutions
- Angles B and C and side c for each
- Area of each
Interpreting the result
- Two solutions mean two possible shapes (for example two positions of a link); pick the one that matches the design.
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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Open the Triangle from Two Sides and an Opposite Angle calculator
