Law of Sines Calculator

Solve a triangle using the sine rule: a/sin A = b/sin B = c/sin C.

About Law of Sines Calculator

The Law of Sines states that in any triangle, each side divided by the sine of its opposite angle is constant: a/sin A = b/sin B = c/sin C. It is used to solve triangles when you know AAS or ASA configurations.

Formula

Law of Sines

a / sin A = b / sin B = c / sin C

a: Side opposite angle A
b: Side opposite angle B
c: Side opposite angle C

Worked example

With the default values below, Law of Sines Calculator returns Side b of 10.724622. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side aminimum 0.001: 7
Angle A (degrees, opposite a)accepts 0.01–179.99: 30
Angle B (degrees, opposite b)accepts 0.01–179.99: 50

Results

Side b: 10.724622
Side c: 13.787309
Angle C: 100.000000 °
a/sin A ratio: 14.000000

Step by step

1Find angle C= 100°
2Common ratio= 14
3Find side b= 10.7246222
4Find side c= 13.78730854

Assumptions and limits

The result is derived only from the 3 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 6 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

When do you use Law of Sines vs Law of Cosines?

Use Law of Sines when you know a side and its opposite angle plus one other measurement (AAS, ASA). Use Law of Cosines for SSS or SAS configurations.

What is the ambiguous case?

When given two sides and an angle opposite one (SSA), the Law of Sines may yield 0, 1, or 2 valid triangles because arcsin can have two solutions.