Triangle Trigonometry Solver
Solve any triangle given three known values (SSS, SAS, ASA, AAS) using trig laws.
About Triangle Trigonometry Solver
This solver handles any triangle (right or oblique) using the Law of Cosines for SSS/SAS and the Law of Sines for ASA/AAS. It reports all sides, angles, area and perimeter.
Formulas
Law of Cosines
c² = a² + b² − 2ab·cos C
- a
- Side a
- b
- Side b
- c
- Side c
- C
- Angle opposite c
Law of Sines
a/sin A = b/sin B = c/sin C
- a
- Side a
- A
- Angle opposite a
Area
Area = ½ · a · b · sin C
- a
- Side a
- b
- Side b
- C
- Included angle
Worked example
With the default values below, Triangle Trigonometry Solver returns Area of 15.1554. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Configurationone of SAS (two sides + included angle), SSS (three sides), ASA (two angles + included side), AAS (two angles + non-included side)
- SAS (two sides + included angle)
- Side aminimum 0.001
- 5
- Side bminimum 0.001
- 7
- Side c (between A and B)minimum 0.001
- 8
- Angle A (°)accepts 0.01–179.99
- 40
- Angle B (°)accepts 0.01–179.99
- 60
- Angle C (°, between a and b)accepts 0.01–179.99
- 60
Results
- Area
- 15.1554
- Side a
- 5.0000
- Side b
- 7.0000
- Side c
- 6.2450
- Angle A
- 43.8979 °
- Angle B
- 76.1021 °
- Angle C
- 60.0000 °
- Perimeter
- 18.2450
Step by step
- 1Sides= a=5, b=7, c=6.245
- 2Angles= A=43.8979°, B=76.1021°, C=60°
- 3Area= 15.155445
Assumptions and limits
- The result is derived only from the 7 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Which configuration should I choose?
SSS if you know all three sides, SAS if you know two sides and the angle between them, ASA if you know two angles and the side between them, AAS if you know two angles and a non-included side.
Can this solve a right triangle?
Yes — a right triangle is a special case. Enter 90° as one angle in ASA/AAS mode, or enter two legs and 90° in SAS mode.