Solve Oblique Triangle Calculator

Work out solve oblique triangle instantly with clear inputs, formula shown and shareable results.

About Solve Oblique Triangle Calculator

An oblique triangle has no right angle, so the law of cosines does the work: cos A = (b² + c² − a²)/(2bc). In SAS mode the missing side is found first from a² = b² + c² − 2bc·cos A, then the angles follow.

Formulas

Law of cosines

a² = b² + c² − 2bc·cos A, cos A = (b² + c² − a²) / (2bc)

Heron's area

Area = √[s(s−a)(s−b)(s−c)]

Worked example

With the default values below, Solve Oblique Triangle Calculator returns Angle A of 33.5573. Change any input above and every figure here is recalculated in your browser.

Inputs used

What you knowone of Three sides (SSS), Two sides and the included angle (SAS): Three sides (SSS)
Side bminimum 0: 7
Side cminimum 0: 9
Side a (SSS) or included angle A in ° (SAS)minimum 0: 5

Results

Angle A: 33.5573 °
Angle B: 50.7035 °
Angle C: 95.7392 °
Area: 17.4123

Step by step

1Values used
2Law of cosines
3Heron's area
4Angle A= 33.5573 °
5Angle B= 50.7035 °
6Angle C= 95.7392 °
7Area= 17.4123

Assumptions and limits

The result is derived only from the 4 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

For sides 5, 7, 9?

cos A = (49 + 81 − 25)/126 = 105/126, giving A ≈ 33.5573°, B ≈ 50.7035°, C ≈ 95.7393°.

Why avoid the law of sines for angles?

Arcsine cannot distinguish an angle from its supplement, so the law of cosines is safer when the triangle may be obtuse.