When should I use the law of sines?

Use it when you know an opposite side-angle pair and need to solve an ASA, AAS, or SSA triangle.

What is the SSA ambiguous case?

SSA data can produce two possible triangles, one triangle, or no triangle depending on the side lengths and the given angle.

Does the law of sines work for right triangles?

Yes, but right-triangle SOH-CAH-TOA methods may be simpler when a 90-degree angle is known.

Do angles need to add to 180 degrees?

Yes. A valid Euclidean triangle has interior angles summing to 180 degrees.

Law of Sines Calculator

Solve triangles with the law of sines for ASA, AAS, and SSA cases, including the ambiguous case when two triangle solutions are possible.

Law of Sines Calculator

Solve triangles with AAS, ASA, and SSA inputs, including the ambiguous SSA case. A separate mode calculates circumradius from a side and its opposite angle.

Enter two angles and the side opposite the first angle.

Angle A (degrees)

Angle B (degrees)

Side opposite angle A

Solution

Angle A

60°

Angle B

80°

Angle C

40°

Side opposite angle A

Side opposite angle B

11.3716

Side opposite angle C

7.4223

Perimeter

28.7939

Area

36.5476

Circumradius

5.7735

Result Check

Angle sum

180°

Perimeter

28.7939

Area

36.5476

Solve triangles with the law of sines

Law of sines search intent is a triangle solver: use a known side-angle opposite pair to find missing sides or angles, especially ASA, AAS, and SSA triangle problems.

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

a, b, and c are sides opposite angles A, B, and C.

SSA ambiguous case

When two sides and a non-included angle are known, the SSA case can produce zero, one, or two valid triangles. A useful English law-of-sines calculator should show that ambiguity instead of hiding it.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

Related Tools

Sin Cos Tan Calculator

Calculate sine, cosine, tangent, cotangent, secant, and cosecant for an angle in degrees, radians, pi-radians, or DMS, with exact unit-circle values when available.

Open

Inverse Trig Calculator

Calculate arcsin, arccos, and arctan values with principal-angle results in degrees and radians, plus domain checks for inverse sine and cosine.

Open

Triangle Area Calculator

Calculate triangle area from base and height, three sides, two sides and an included angle, angles and a side, coordinates, right-triangle legs, or circle radii with three sides.

Open

Triangle Perimeter Calculator

Calculate triangle perimeter from three sides, one equilateral side, equal side and base, or two right-triangle legs with triangle inequality checks.

Open